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Journal articles on the topic 'Linear stochastic dynamic systems'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Klamka, Jerzy. "Stochastic Controllability of Linear Systems With State Delays." International Journal of Applied Mathematics and Computer Science 17, no. 1 (2007): 5–13. http://dx.doi.org/10.2478/v10006-007-0001-8.

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Stochastic Controllability of Linear Systems With State DelaysA class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic

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2

Klamka, Jerzy. "Stochastic Controllability of Systems with Multiple Delays in Control." International Journal of Applied Mathematics and Computer Science 19, no. 1 (2009): 39–48. http://dx.doi.org/10.2478/v10006-009-0003-9.

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Stochastic Controllability of Systems with Multiple Delays in ControlFinite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relativ

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3

Zhang, Yingqi, Wei Cheng, Xiaowu Mu та Caixia Liu. "Stochasticℋ∞Finite-Time Control of Discrete-Time Systems with Packet Loss". Mathematical Problems in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/897481.

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This paper investigates the stochastic finite-time stabilization andℋ∞control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time

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4

Long, Fei, Hongmei Huang, and Adan Ding. "Stochastic Stabilization of Itô Stochastic Systems with Markov Jumping and Linear Fractional Uncertainty." Journal of Control Science and Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/697849.

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For a class of Itô stochastic linear systems with the Markov jumping and linear fractional uncertainty, the stochastic stabilization problem is investigated via state feedback and dynamic output feedback, respectively. In order to guarantee the stochastic stability of such uncertain systems, state feedback and dynamic output control law are, respectively, designed by using multiple Lyapunov function technique and LMI approach. Finally, two numerical examples are presented to illustrate our results.

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5

Javadi, Ali, Mohammad Reza Jahed-Motlagh, and Ali Akbar Jalali. "Robust H∞ control of stochastic linear systems with input delay by predictor feedback." Transactions of the Institute of Measurement and Control 40, no. 7 (2017): 2396–407. http://dx.doi.org/10.1177/0142331217708241.

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This study investigates the prediction-based (dynamic) stabilization of linear systems with input delay in the presence of external disturbances and multiplicative noise modelled as Itô type stochastic differential equations. Conventional memory-less (static) controllers are widely used for the stabilization of both deterministic and stochastic delayed systems. However, using these methods the upper bound for delay is strongly restricted. Motivated by acceptable performances of dynamic controllers for deterministic delayed systems, the extension of these methods for stochastic delayed systems

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6

SUN, L., and B. S. GREENBERG. "DYNAMIC RESPONSE OF LINEAR SYSTEMS TO MOVING STOCHASTIC SOURCES." Journal of Sound and Vibration 229, no. 4 (2000): 957–72. http://dx.doi.org/10.1006/jsvi.1999.2519.

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7

Lukashiv, Taras, Igor V. Malyk, Ahmed Abdelmonem Hemedan, and Venkata P. Satagopam. "Optimal Control of Stochastic Dynamic Systems with Semi-Markov Parameters." Symmetry 17, no. 4 (2025): 498. https://doi.org/10.3390/sym17040498.

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This paper extends classical Markov switching models. We introduce a generalized semi-Markov switching framework in which the system dynamics are governed by an Itô stochastic differential equation. Of note, the optimal control synthesis problem is formulated for stochastic dynamic systems with semi-Markov parameters. Further, a system of ordinary differential equations is derived to characterize the Bellman functional and the corresponding optimal control. We investigate the case of linear dynamics in detail, and propose a closed-form solution for the optimal control law. A numerical example

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8

Rathore, Sandhya, Shambhu N. Sharma, Dhruvi Bhatt, and Shaival Nagarsheth. "Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective." Transactions of the Institute of Measurement and Control 42, no. 10 (2020): 1755–68. http://dx.doi.org/10.1177/0142331219895711.

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Bilinear stochastic differential equations have found applications to model turbulence in autonomous systems as well as switching uncertainty in non-linear dynamic circuits. In signal processing and control literature, bilinear stochastic differential equations are ubiquitous, since they capture non-linear qualitative characteristics of dynamic systems as well as offer closed-form solutions. The novelties of the paper are two: we weave bilinear filtering for the Stratonovich stochasticity. Then this paper unfolds the usefulness of bilinear filtering for switched dynamic systems. First, the Str

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9

Zhang, Huasheng, Changan Shao, Han Geng, and Tingting Zhang. "A Precise Stabilization Method for Linear Stochastic Time-Delay Systems." Actuators 11, no. 11 (2022): 325. http://dx.doi.org/10.3390/act11110325.

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Based on ensuring the steady-state performance of the system, some dynamic performance indicators that have not yet been realized in linear stochastic systems with time-delay are discussed in this paper. First, in view of the relationship between system eigenvalues and system performances, the region stability is provided, which can reflect the dynamic performance of the systems. Second, the design scheme of the region stabilization controller is given based on the region stability, so that the closed-loop system has the corresponding dynamic performance. Third, this paper also designs an algo

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10

Chang, R. J. "Two-stage optimal stochastic linearization in analyzing of non-linear stochastic dynamic systems." International Journal of Non-Linear Mechanics 58 (January 2014): 295–304. http://dx.doi.org/10.1016/j.ijnonlinmec.2013.10.002.

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11

Hayawi, Heyam A. A., Najlaa Saad Ibrahim, and Lamyaa Jasim Mohammed. "Using the fuzzy technique to identification stochastic linear dynamic systems." Journal of Statistics and Management Systems 24, no. 4 (2021): 801–8. http://dx.doi.org/10.1080/09720510.2020.1859808.

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12

El-ghatwary, Magdy G., and Steven X. Ding. "Robust Fuzzy Fault Detection for Non-Linear Stochastic Dynamic Systems." Open Automation and Control Systems Journal 2, no. 1 (2009): 45–53. http://dx.doi.org/10.2174/1874444300902010045.

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13

El-ghatwary, Magdy G., and Steven X. Ding. "Robust Fuzzy Fault Detection for Non-Linear Stochastic Dynamic Systems." Open Automation and Control Systems Journal 2, no. 2 (2009): 45–53. http://dx.doi.org/10.2174/1874444300902020045.

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14

Samarin, A. I. "Problem of Consensus for Linear Dynamic Systems with Stochastic Disturbances." Moscow University Computational Mathematics and Cybernetics 45, no. 1 (2021): 21–33. http://dx.doi.org/10.3103/s0278641921010052.

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15

Azemi, Asad, and Engin Yaz. "Dynamic disturbance minimization control for discrete non-linear stochastic systems." Optimal Control Applications and Methods 14, no. 3 (1993): 181–94. http://dx.doi.org/10.1002/oca.4660140304.

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16

Agrawal, O. P. "Application of Wavelets in Modeling Stochastic Dynamic Systems." Journal of Vibration and Acoustics 120, no. 3 (1998): 763–69. http://dx.doi.org/10.1115/1.2893895.

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This paper presents a wavelet based model for stochastic dynamic systems. In this model, the state variables and their variations are approximated using truncated linear sums of orthogonal polynomials, and a modified Hamilton’s law of varying action is used to reduce the integral equations representing dynamics of the system to a set of algebraic equations. For deterministic systems, the coefficients of the polynomials are constant, but for stochastic systems, the coefficients are random variables. The external forcing functions are treated as stationary Gaussian processes with specified mean

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17

Francisco, Gerson, Cláudio Paiva, and Rogerio Rosenfeld. "Dynamic parameters for Brazilian financial time series." Economia Aplicada 6, no. 1 (2002): 67–77. https://doi.org/10.11606/1413-8050/ea219890.

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In this study we analyse a Brazilian stock index called IBOVESPA using techniques from dynamical systems theory and stochastic processes. We discuss the Lyapunov exponent, the correlation dimension, the LempelZiv complexity, the Hurst exponent and the BDS statistics. We compare this study with other time series including stock prices and deterministic systems. We conclude that the IBOVESPA is a linear stochastic process that exhibits the phenomenon of persistence, thatis, it has long term memory. The stocks are described by nonlinear stochastic processes making it impossible to be simulated wi

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18

Marti, Kurt. "Duality in stochastic linear and dynamic programming." European Journal of Operational Research 31, no. 3 (1987): 392–93. http://dx.doi.org/10.1016/0377-2217(87)90055-5.

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19

Sorokin, V., and I. Demidov. "On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2192 (2021): 20200229. http://dx.doi.org/10.1098/rsta.2020.0229.

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Adding noise to a system can ‘improve’ its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the a

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20

Siu, D. P., and G. S. Ladde. "A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution." Journal of Probability and Statistics 2011 (2011): 1–20. http://dx.doi.org/10.1155/2011/720614.

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In this work, a class of multidimensional stochastic hybrid dynamic models is studied. The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the systems are obtained. Furthermore, the major part of the work is devoted to finding closed-form probability density functions of the solution processes of linear homogeneous and Ornstein-Uhlenbeck type system

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21

Liu, Kaiwei, Bing Yuan, and Jiang Zhang. "An Exact Theory of Causal Emergence for Linear Stochastic Iteration Systems." Entropy 26, no. 8 (2024): 618. http://dx.doi.org/10.3390/e26080618.

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After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian nois

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22

Hu, R. C., X. F. Wang, X. D. Gu, and R. H. Huan. "Nonlinear Stochastic Optimal Control of MDOF Partially Observable Linear Systems Excited by Combined Harmonic and Wide-Band Noises." International Journal of Structural Stability and Dynamics 19, no. 03 (2019): 1950019. http://dx.doi.org/10.1142/s0219455419500196.

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In this paper, nonlinear stochastic optimal control of multi-degree-of-freedom (MDOF) partially observable linear systems subjected to combined harmonic and wide-band random excitations is investigated. Based on the separation principle, the control problem of a partially observable system is converted into a completely observable one. The dynamic programming equation for the completely observable control problem is then set up based on the stochastic averaging method and stochastic dynamic programming principle, from which the nonlinear optimal control law is derived. To illustrate the feasib

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23

Ge, Zhaoqiang. "Linear Quadratic Optimal Control Problem for Linear Stochastic Generalized System in Hilbert Spaces." Mathematics 10, no. 17 (2022): 3118. http://dx.doi.org/10.3390/math10173118.

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A finite-horizon linear stochastic quadratic optimal control problem is investigated by the GE-evolution operator in the sense of the MILS solution in Hilbert spaces. We assume that the coefficient operator of the differential term is a bounded linear operator and that the state and input operators are time-varying in the dynamic equation of the problem. Optimal state feedback along with the well-posedness of the generalized Riccati equation is obtained for the finite-horizon case. The results are also applicable to the linear quadratic optimal control problem of ordinary time-varying linear s

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24

Liu, Yan, Weifeng Zhong, Qiang Fan, Bo You, and Jiazhong Xu. "Robust Observer Design for Discrete Descriptor Systems with Packet Losses." Complexity 2021 (January 31, 2021): 1–11. http://dx.doi.org/10.1155/2021/2505043.

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This paper considers observer design for discrete-time descriptor systems with packet losses. By taking packet loss into consideration, the error dynamic of the proposed observer becomes a stochastic switched system. Consequently, the proposed observer is synthesized in a stochastic switched system framework. Sufficient conditions for the stochastic stability with a prescribed robust performance of the error dynamic system are derived and converted into linear matrix inequalities. Not only can the proposed observer deal with packet losses, but it also attenuates the effect of process disturban

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25

Pradlwarter, H. J., and G. I. Schuëller. "Reliability of deterministic non-linear systems subjected to stochastic dynamic excitation." International Journal for Numerical Methods in Engineering 85, no. 9 (2010): 1160–76. http://dx.doi.org/10.1002/nme.3017.

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26

Chen, Yan, Yingchun Deng, Shengjie Yue, and Chao Deng. "Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience." Advances in Mathematical Physics 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/8730859.

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This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts

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27

Petrik, Marek, and Shlomo Zilberstein. "Linear Dynamic Programs for Resource Management." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (2011): 1377–83. http://dx.doi.org/10.1609/aaai.v25i1.7794.

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Sustainable resource management in many domains presents large continuous stochastic optimization problems, which can often be modeled as Markov decision processes (MDPs). To solve such large MDPs, we identify and leverage linearity in state and action sets that is common in resource management. In particular, we introduce linear dynamic programs (LDPs) that generalize resource management problems and partially observable MDPs (POMDPs). We show that the LDP framework makes it possible to adapt point-based methods--the state of the art in solving POMDPs--to solving LDPs. The experimental result

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28

Orellana, Rafael, Rodrigo Carvajal, Pedro Escárate, and Juan C. Agüero. "On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian Mixture Models." Sensors 21, no. 11 (2021): 3837. http://dx.doi.org/10.3390/s21113837.

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In control and monitoring of manufacturing processes, it is key to understand model uncertainty in order to achieve the required levels of consistency, quality, and economy, among others. In aerospace applications, models need to be very precise and able to describe the entire dynamics of an aircraft. In addition, the complexity of modern real systems has turned deterministic models impractical, since they cannot adequately represent the behavior of disturbances in sensors and actuators, and tool and machine wear, to name a few. Thus, it is necessary to deal with model uncertainties in the dyn

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29

Yakup, H. HACI, CANDAN Muhammet, and OR Aykut. "On the Principle of Optimality for Linear Stochastic Dynamic System." International Journal on Foundations of Computer Science & Technology (IJFCST) 6, no. 1 (2023): 7. https://doi.org/10.5281/zenodo.7524710.

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In this work, processes represented by linear stochastic dynamic system are investigated and by considering optimal control problem, principle of optimality is proven. Also, for existence of optimal control and corresponding optimal trajectory, proofs of theorems of necessity and sufficiency condition are attained.

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30

Fan, Wei (David). "Management of Dynamic Vehicle Allocation for Carsharing Systems." Transportation Research Record: Journal of the Transportation Research Board 2359, no. 1 (2013): 51–58. http://dx.doi.org/10.3141/2359-07.

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Carsharing offers innovative mobility solutions and has been gaining popularity around the world as an environmentally sustainable, socially responsible, and economically feasible form of mobility. Carsharing allows members to benefit from private vehicle use without the costs and responsibilities of ownership and provides individuals with access to a fleet of shared-use vehicles in a network of locations on a short-term, as-needed basis. This paper seeks to develop a stochastic optimization framework to address the dynamic vehicle allocation problem for carsharing systems, in which the servic

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31

Lukashiv, Taras, Igor V. Malyk, Venkata P. Satagopam, and Petr V. Nazarov. "Stabilization of Stochastic Dynamic Systems with Markov Parameters and Concentration Point." Mathematics 13, no. 14 (2025): 2307. https://doi.org/10.3390/math13142307.

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This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapt

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32

Tronarp, Filip, and Simo Särkkä. "Iterative statistical linear regression for Gaussian smoothing in continuous-time non-linear stochastic dynamic systems." Signal Processing 159 (June 2019): 1–12. http://dx.doi.org/10.1016/j.sigpro.2019.01.013.

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33

Fernandez, Javier H., Jason L. Speyer, and Moshe Idan. "Stochastic Estimation for Two-State Linear Dynamic Systems With Additive Cauchy Noises." IEEE Transactions on Automatic Control 60, no. 12 (2015): 3367–72. http://dx.doi.org/10.1109/tac.2015.2422478.

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34

Wang, Honggang. "Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation." European Journal of Operational Research 217, no. 1 (2012): 141–48. http://dx.doi.org/10.1016/j.ejor.2011.08.020.

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35

Baczynski, Jack, Marcelo D. Fragoso, and Ernesto P. Lopes. "On a discrete-time linear jump stochastic dynamic game." International Journal of Systems Science 32, no. 8 (2001): 979–88. http://dx.doi.org/10.1080/00207720118956.

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36

Punčochár, Ivo, and Miroslav Šmandl. "On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems." International Journal of Applied Mathematics and Computer Science 24, no. 4 (2014): 795–807. http://dx.doi.org/10.2478/amcs-2014-0059.

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Abstract The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dyna

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37

Wu, Jiang, Fucheng Liao, and Jiamei Deng. "Optimal Preview Control for a Class of Linear Continuous Stochastic Control Systems in the Infinite Horizon." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/7679165.

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This paper discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system. Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking problem is converted to a regulation problem. Secondly, the optimal regulator is solved based on dynamic programming principle for the stochastic system, and the optimal preview controller of the origi

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38

Gang, Ting-Ting, Jun Yang, Qing Gao, Yu Zhao, and Jianbin Qiu. "A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/439805.

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This paper investigates the stabilization problem for a class of discrete-time stochastic non-affine nonlinear systems based on T-S fuzzy models. Based on the function approximation capability of a class of stochastic T-S fuzzy models, it is shown that the stabilization problem of a stochastic non-affine nonlinear system can be solved as a robust stabilization problem of the stochastic T-S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilizatio

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39

Heitmann, Stewart, and Michael Breakspear. "Putting the “dynamic” back into dynamic functional connectivity." Network Neuroscience 2, no. 2 (2018): 150–74. http://dx.doi.org/10.1162/netn_a_00041.

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The study of fluctuations in time-resolved functional connectivity is a topic of substantial current interest. As the term “dynamic functional connectivity” implies, such fluctuations are believed to arise from dynamics in the neuronal systems generating these signals. While considerable activity currently attends to methodological and statistical issues regarding dynamic functional connectivity, less attention has been paid toward its candidate causes. Here, we review candidate scenarios for dynamic (functional) connectivity that arise in dynamical systems with two or more subsystems; general

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40

Zhang, Weihai, Bor-Sen Chen, Li Sheng, and Ming Gao. "RobustH2/H∞Filter Design for a Class of Nonlinear Stochastic Systems with State-Dependent Noise." Mathematical Problems in Engineering 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/750841.

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This paper investigates the problem of robust filter design for a class of nonlinear stochastic systems with state-dependent noise. The state and measurement are corrupted by stochastic uncertain exogenous disturbance and the dynamic system is modeled by Itô-type stochastic differential equations. For this class of nonlinear stochastic systems, the robustH∞filter can be designed by solving linear matrix inequalities (LMIs). Moreover, a mixedH2/H∞filtering problem is also solved by minimizing the total estimation error energy when the worst-case disturbance is considered in the design procedure

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41

Gurt, Assaf, and Girish N. Nair. "Internal stability of dynamic quantised control for stochastic linear plants." Automatica 45, no. 6 (2009): 1387–96. http://dx.doi.org/10.1016/j.automatica.2009.02.016.

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42

Delavarkhalafi, A., and A. Poursherafatan. "Filtering method for linear and non-linear stochastic optimal control of partially observable systems." Filomat 31, no. 19 (2017): 5979–92. http://dx.doi.org/10.2298/fil1719979d.

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This paper studies two linear methods for linear and non-linear stochastic optimal control of partially observable problem (SOCPP). At first, it introduces the general form of a SOCPP and states it as a functional matrix. A SOCPP has a payoff function which should be minimized. It also has two dynamic processes: state and observation. In this study, it is presented a deterministic method to find the control factor which has named feedback control and stated a modified complete proof of control optimality in a general SOCPP. After finding the optimal control factor, it should be substituted in

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43

Bhatt, Dhruvi S., Shaival H. Nagarsheth, and Shambhu N. Sharma. "On the Theory of a Nonlinear Dynamic Circuit Filtering." Fluctuation and Noise Letters 19, no. 03 (2020): 2050022. http://dx.doi.org/10.1142/s0219477520500224.

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Stochastic Differential Equations (SDEs) describe physical systems to account for random forcing terms in the evolution of the state trajectory. The noisy sampling mixer, a component of digital wireless communications, can be regarded as a potential case from the dynamical systems’ viewpoint. The universality of the noisy sampling mixer is attributed to the fact that it adopts the structure of a nonlinear SDE and its linearized version becomes a time-varying bilinear SDE. This paper develops a mathematical theory for the nonlinear noisy sampling mixer from the filtering viewpoint. Since the fi

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44

Ding, Yu Cai, Hong Zhu, Yu Ping Zhang, and Yong Zeng. "Robust Stabilization of Stochastic Singular Systems with Markovian Switching." Advanced Materials Research 591-593 (November 2012): 1496–501. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.1496.

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In this paper, robust stability and stabilization of singular stochastic hybrid systems are investigated. The system under consideration involves parameter uncertainties, Itô-type stochastic disturbance, Markovian jump parameters as well as time-varying delays. The aim of this paper is to design a state controller such that the dynamic system is robust stable. By using the Lyapunov-Krasovskii functional and Itô's differential rule, delay-range-dependent sufficient conditions on robust stability and stabilization are obtained in the form of linear matrix inequalities (LMIs). A numerical example

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45

Sarker, Arnab, Peter Fisher, Joseph Gaudio, and Anuradha Annaswamy. "Accurate Parameter Estimation for Safety-Critical Systems with Unmodeled Dynamics (Abstract Reprint)." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 20 (2024): 22711. http://dx.doi.org/10.1609/aaai.v38i20.30611.

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Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. Much of feedback control design is parametric in nature and as such, accurate and fast estimation of the parameters in the modeled part of the dynamic system is a crucial property for designing risk-aware autonomous systems. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unm

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46

Tellier, M., and R. Iwankiewicz. "Response of linear dynamic systems to non-Erlang renewal impulses: Stochastic equations approach." Probabilistic Engineering Mechanics 20, no. 4 (2005): 281–95. http://dx.doi.org/10.1016/j.probengmech.2005.05.006.

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47

Grigoriu, M. "Solution of linear dynamic systems with uncertain properties by stochastic reduced order models." Probabilistic Engineering Mechanics 34 (October 2013): 168–76. http://dx.doi.org/10.1016/j.probengmech.2013.09.001.

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48

Foster, Dallas, and Juan M. Restrepo. "An improved framework for the dynamic likelihood filtering approach to data assimilation." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 5 (2022): 053118. http://dx.doi.org/10.1063/5.0083071.

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We propose improvements to the Dynamic Likelihood Filter (DLF), a Bayesian data assimilation filtering approach, specifically tailored to wave problems. The DLF approach was developed to address the common challenge in the application of data assimilation to hyperbolic problems in the geosciences and in engineering, where observation systems are sparse in space and time. When these observations have low uncertainties, as compared to model uncertainties, the DLF exploits the inherent nature of information and uncertainties to propagate along characteristics to produce estimates that are phase a

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He, Shuping, and Fei Liu. "RobustL2-L∞Filtering of Time-Delay Jump Systems with Respect to the Finite-Time Interval." Mathematical Problems in Engineering 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/839648.

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This paper studied the problem of stochastic finite-time boundedness and disturbance attenuation for a class of linear time-delayed systems with Markov jumping parameters. Sufficient conditions are provided to solve this problem. TheL2-L∞filters are, respectively, designed for time-delayed Markov jump linear systems with/without uncertain parameters such that the resulting filtering error dynamic system is stochastically finite-time bounded and has the finite-time interval disturbance attenuationγfor all admissible uncertainties, time delays, and unknown disturbances. By using stochastic Lyapu

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Savla, Ketan, Jeff S. Shamma, and Munther A. Dahleh. "Network Effects on the Robustness of Dynamic Systems." Annual Review of Control, Robotics, and Autonomous Systems 3, no. 1 (2020): 115–49. http://dx.doi.org/10.1146/annurev-control-091219-012549.

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We review selected results related to the robustness of networked systems in finite and asymptotically large size regimes in static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss the effect of physical constraints on robustness to loss in link capacities. In the dynamical setting, we review several settings in which small-gain-type analysis provides tight robustness guarantees for linear dynamics over finite networks toward worst-case and stochastic disturbances. We discuss network flow dynamic settings where nonlinear techniques fa

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