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Journal articles on the topic 'Lyapunov stability'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 November 2024

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1

Lakshmikantham, V., X. Liu, and S. Leela. "Variational Lyapunov method and stability theory." Mathematical Problems in Engineering 3, no. 6 (1998): 555–71. http://dx.doi.org/10.1155/s1024123x97000689.

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By unifying the method of variation of parameters and Lyapunov's second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing the advantage of this unification.

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2

Ates, Muzaffer, and Nezir Kadah. "Novel stability and passivity analysis for three types of nonlinear LRC circuits." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 11, no. 2 (July 31, 2021): 227–37. http://dx.doi.org/10.11121/ijocta.01.2021.001073.

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In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The results are provided within and are of central importance for the analysis of nonlinear electrical, mechanical, and neural systems which based on the system energy perspective. The simulation results given from Matlab successfully verifies the theoretical predictions.

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3

Bomze, Immanuel M., and Jörgen W. Weibull. "Does Neutral Stability Imply Lyapunov Stability?" Games and Economic Behavior 11, no. 2 (November 1995): 173–92. http://dx.doi.org/10.1006/game.1995.1048.

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4

Justus, James. "Ecological and Lyapunov Stability*." Philosophy of Science 75, no. 4 (October 2008): 421–36. http://dx.doi.org/10.1086/595836.

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5

Ledrappier, F., and L. S. Young. "Stability of Lyapunov exponents." Ergodic Theory and Dynamical Systems 11, no. 3 (September 1991): 469–84. http://dx.doi.org/10.1017/s0143385700006283.

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AbstractWe consider small random perturbations of matrix cocycles over Lipschitz homeomorphisms of compact metric spaces. Lyapunov exponents are shown to be stable provided that our perturbations satisfy certain regularity conditions. These results are applicable to dynamical systems, particularly to volume-preserving diffeomorphisms.

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6

Kunitsyn, A. L., and V. N. Tkhai. "Stability in Lyapunov systems." Journal of Applied Mathematics and Mechanics 70, no. 4 (January 2006): 497–503. http://dx.doi.org/10.1016/j.jappmathmech.2006.09.003.

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7

Liu, Yunping, Xijie Huang, Yonghong Zhang, and Yukang Zhou. "Dynamic Stability and Control of a Manipulating Unmanned Aerial Vehicle." International Journal of Aerospace Engineering 2018 (June 12, 2018): 1–13. http://dx.doi.org/10.1155/2018/3481328.

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This paper focuses on the dynamic stability analysis of a manipulator mounted on a quadrotor unmanned aerial vehicle, namely, a manipulating unmanned aerial vehicle (MUAV). Manipulator movements and environments interaction will extremely affect the dynamic stability of the MUAV system. So the dynamic stability analysis of the MUAV system is of paramount importance for safety and satisfactory performance. However, the applications of Lyapunov’s stability theory to the MUAV system have been extremely limited, due to the lack of a constructive method available for deriving a Lyapunov function. Thus, Lyapunov exponent method and impedance control are introduced, and the Lyapunov exponent method can establish the quantitative relationships between the manipulator movements and the dynamics stability, while impedance control can reduce the impact of environmental interaction on system stability. Numerical simulation results have demonstrated the effectiveness of the proposed method.

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8

Yunping, Liu, Wang Lipeng, Mei Ping, and Hu Kai. "Stability Analysis of Bipedal Robots Using the Concept of Lyapunov Exponents." Mathematical Problems in Engineering 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/546520.

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The dynamics and stability of passive bipedal robot have an important impact on the mass distribution, leg length, and the angle of inclination. Lyapunov’s second method is difficult to be used in highly nonlinear multibody systems, due to the lack of constructive methods for deriving Lyapunov fuction. The dynamics equation is established by Kane method, the relationship between the mass, length of leg, angle of inclination, and stability of passive bipedal robot by the largest Lyapunov exponent. And the Lyapunov exponents of continuous dynamical systems are estimated by numerical methods, which are simple and easy to be applied to the system stability simulation analysis, provide the design basis for passive bipedal robot prototype, and improve design efficiency.

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9

Beisenbi, Мamyrbek, and Samal Kaliyeva. "Approach to the synthesis of an aperiodic robust automatic control system based on the gradient-speed method of Lyapunov vector functions." Eastern-European Journal of Enterprise Technologies 1, no. 3 (121) (February 28, 2023): 6–14. http://dx.doi.org/10.15587/1729-4061.2023.274063.

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One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements

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10

Kostrub, Irina Dmitrievna. "HURWITZ MATRIX, LYAPUNOV AND DIRICHLET ON THE SUSTAINABILITY OF LYAPUNOV’S." Tambov University Reports. Series: Natural and Technical Sciences, no. 123 (2018): 431–36. http://dx.doi.org/10.20310/1810-0198-2018-23-123-431-436.

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The concepts of Hurwitz, Lyapunov and Dirichlet matrices are introduced for the convenience of the stability of linear systems with constant coefficients. They allow us to describe all the cases of interest in the stability theory of linear systems with constant coefficients. A similar classification is proposed for systems of linear differential equations with periodic coefficients. Monodromy matrices of such systems can be either Hurwitz matrices or Lyapunov matrices or Dirichlet matrices (in the discrete sense) in a stable case. The new material relates to systems with variable coefficients.

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11

Martynyuk, Anatoly A. "Analysis of stability problems via matrix Lyapunov functions." Journal of Applied Mathematics and Stochastic Analysis 3, no. 4 (January 1, 1990): 209–26. http://dx.doi.org/10.1155/s104895339000020x.

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The stability of nonlinear systems is analyzed by the direct Lyapunov's method in terms of Lyapunov matrix functions. The given paper surveys the main theorems on stability, asymptotic stability and nonstability. They are applied to systems of nonlinear equations, singularly-perturbed systems and hybrid systems. The results are demonstrated by an example of a two-component system.

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12

Zhao, Rongyong, Ping Jia, Yan Wang, Cuiling Li, Yunlong Ma, and Zhishu Zhang. "Acceleration-critical density time-delay model for crowd stability analysis based on Lyapunov theory." MATEC Web of Conferences 355 (2022): 03019. http://dx.doi.org/10.1051/matecconf/202235503019.

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Crowd stability analysis is one of research hotspots to alleviate the severe situation of stampede accidents worldwide. Different from the conventional analysis models for crowd stability based on pedestrian density, this study analyses the characteristics of external disturbances and internal obstacle disturbance based on Lyapunov's theory. The critical range of crowd acceleration in crowd evacuation is obtained, a crowd merging acceleration-critical density time delay model is established, and a stability criterion of acceleration vector based on Lyapunov is obtained based on Lyapunov stability analysis. This provides new information for ensuring the stability of crowd movement in public places, assessing the stability of the crowd in the area, and taking reasonable protection and guidance measures prior to instability of a crowd flow.

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13

Santos, Iguer. "Lyapunov stability for discontinuous systems." Ciência e Natura 42 (May 15, 2020): e17. http://dx.doi.org/10.5902/2179460x42344.

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The present work studies the stability analysis of equilibrium of ordinary differential equations with the discontinuous right side, also called discontinuous differential equations, using the notion of Carathéodory solution for differential equations. This way, it is studied the stability of equilibrium in the Lyapunov sense for discontinuous systems through nonsmooth Lyapunov functions. Then two existing Lyapunov theorems are obtained. The results established refer to systems determined by nonautonomous differential equations.

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14

Romm, Ya E., and S. G. Bulanov. "NUMERICAL MODELING OF LYAPUNOV STABILITY." Современные наукоемкие технологии (Modern High Technologies), no. 7 2021 (2021): 42–60. http://dx.doi.org/10.17513/snt.38752.

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15

Lamperski, Andrew, and Aaron D. Ames. "Lyapunov Theory for Zeno Stability." IEEE Transactions on Automatic Control 58, no. 1 (January 2013): 100–112. http://dx.doi.org/10.1109/tac.2012.2208292.

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16

Redkar, Sangram. "Lyapunov Stability of Quasiperiodic Systems." Mathematical Problems in Engineering 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/721382.

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We present some observations on the stability and reducibility of quasiperiodic systems. In a quasiperiodic system, the periodicity of parametric excitation is incommensurate with the periodicity of certain terms multiplying the state vector. We present a Lyapunov-type approach and the Lyapunov-Floquet (L-F) transformation to derive the stability conditions. This approach can be utilized to investigate the robustness, stability margin, and design controller for the system.

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17

Charron, R. J. "Lyapunov stability via differential moments." Quarterly of Applied Mathematics 49, no. 3 (January 1, 1991): 447–52. http://dx.doi.org/10.1090/qam/1121677.

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18

Michalak, Anna. "Dual approach to Lyapunov stability." Nonlinear Analysis: Theory, Methods & Applications 85 (July 2013): 174–79. http://dx.doi.org/10.1016/j.na.2013.02.007.

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19

Barros, Carlos J. Braga, Josiney A. Souza, and Victor H. L. Rocha. "Lyapunov stability on fiber bundles." Bulletin of the Brazilian Mathematical Society, New Series 46, no. 2 (June 2015): 181–204. http://dx.doi.org/10.1007/s00574-015-0090-1.

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20

Braga Barros, Carlos J., Josiney A. Souza, and Victor H. L. Rocha. "Lyapunov stability for semigroup actions." Semigroup Forum 88, no. 1 (October 24, 2013): 227–49. http://dx.doi.org/10.1007/s00233-013-9527-2.

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21

Barreira, Luis, and Claudia Valls. "Stability theory and Lyapunov regularity." Journal of Differential Equations 232, no. 2 (January 2007): 675–701. http://dx.doi.org/10.1016/j.jde.2006.09.021.

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22

Froyland, Gary, Cecilia González-Tokman, and Anthony Quas. "Hilbert space Lyapunov exponent stability." Transactions of the American Mathematical Society 372, no. 4 (May 20, 2019): 2357–88. http://dx.doi.org/10.1090/tran/7521.

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23

Nikolakopoulos, P. G., and C. A. Papadopoulos. "Lyapunov’s Stability of Nonlinear Misaligned Journal Bearings." Journal of Engineering for Gas Turbines and Power 117, no. 3 (July 1, 1995): 576–81. http://dx.doi.org/10.1115/1.2814134.

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In this paper the stability of nonlinear misaligned rotor-bearing systems is investigated, using the Lyapunov direct method. A finite element formulation is used to determine the journal bearing pressure distribution. Then the linear and nonlinear stiffness, damping, and hybrid (depending on both displacement and velocity) coefficients are calculated. A general method of analysis based on Lyapunov’s stability criteria is used to investigate the stability of nonlinear misaligned rotor bearing systems. The equations of motion of the rigid rotor on the nonlinear bearings are used to find a Lyapunov function using some of these coefficients, which depend on L/D ratio and the misalignment angles ψx, ψy. The analytical conditions for the stability or instability of some examined cases are given and some examples for the orbital stability are also demonstrated.

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24

Miyagi, Norio, and Hayao Miyagi. "Stability of Dynamical Systems With Multiple Nonlinearities." Journal of Dynamic Systems, Measurement, and Control 109, no. 4 (December 1, 1987): 410–13. http://dx.doi.org/10.1115/1.3143875.

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This note applies the direct method of Lyapunov to stability analysis of a dynamical system with multiple nonlinearities. The essential feature of the Lyapunov function used in this note is a non-Lure´ type Lyapunov function which surpasses the Lure´-type Lyapunov function from the point of view of the stability region guaranteed. A modified version of the multivariable Popov criterion is used to construct non-Lure´ type Lyapunov function, which allow for the dynamical sytems with multiple nonlinearities.

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25

Yeh, Ken, and Cheng-Wu Chen. "Stability Analysis of Interconnected Fuzzy Systems Using the Fuzzy Lyapunov Method." Mathematical Problems in Engineering 2010 (2010): 1–10. http://dx.doi.org/10.1155/2010/734340.

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The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist ofJinterconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Some stability conditions are derived through the use of fuzzy Lyapunov functions to ensure that the interconnected fuzzy systems are asymptotically stable. Common solutions can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Finally, simulations are performed in order to verify the effectiveness of the proposed stability conditions in this paper.

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26

Kalitin, B. S. "Lyapunov Stability and Orbital Stability of Dynamical Systems." Differential Equations 40, no. 8 (August 2004): 1096–105. http://dx.doi.org/10.1023/b:dieq.0000049826.73745.c1.

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27

Chu, Chin-Ku, Myung-Sun Kim, and Keon-Hee Lee. "Lipschitz stability and Lyapunov stability in dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 19, no. 10 (November 1992): 901–9. http://dx.doi.org/10.1016/0362-546x(92)90102-k.

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28

DÍAZ-SIERRA, R., and V. FAIRÉN. "NEW METHOD FOR THE ESTIMATION OF DOMAINS OF ATTRACTION OF FIXED POINTS FROM LYAPUNOV FUNCTIONS." International Journal of Bifurcation and Chaos 12, no. 11 (November 2002): 2467–77. http://dx.doi.org/10.1142/s0218127402005984.

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The estimation of the domain of stability of fixed points of nonlinear differential systems constitutes a practical problem of much interest in engineering. The procedures based on Lyapunov's second method configures an alternative worth consideration. It has the appeal of reducing calculation complexity and is time-saving with respect to the direct, computer crunching approach which requires a systematic numerical integration of the evolution equations from a gridlike pattern of initial conditions. However, it is not devoid of problems inasmuch as the Lyapunov function itself is problem-dependent and relies too much on presumptions. Additionally, the evaluation of its corresponding domain is produced in terms of a nonlinear programming problem with inequality constraints the resolution of which may sometimes require a large investment in computer time. These problems are in part avoided by restricting to quadratic Lyapunov functions, with the possible obvious consequence of limiting the estimation of the domain. In order to simplify the estimation of domains we exploit here a novel formulation of the issue of stability of invariant surfaces within Lyapunov's direct method [Díaz-Sierra et al., 2001]. The resulting method addresses directly the optimization problem associated to the evaluation of the stability domain. The problem is recast in a new, simpler form by playing both on the Lyapunov function itself and on the constraints. The gains from the procedure permit to conceive increased returns in the application of Lyapunov's direct method once it is realized that it is not prohibitive from a computational point of view to depart from the limited quadratic Lyapunov functions.

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29

Zhu, Dan, and Debing Ni. "Lyapunov Stability in the Cournot Duopoly Game." Discrete Dynamics in Nature and Society 2023 (March 29, 2023): 1–11. http://dx.doi.org/10.1155/2023/7309724.

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This paper studies Lyapunov stability at a point and its application in the Cournot duopoly game. We first explore the relationship between Lyapunov stability at a point, nonsensitivity and non-Devaney chaos and find that a dynamical system is nonsensitive and non-Devaney chaotic if there is a point in this system such that it is Lyapunov stable at that point. We next prove a group of equivalent characterizations of Lyapunov stability at a point to deduce the composite theorems and product theorems of Lyapunov stability at a point, and then we prove three equivalent characterizations of the Cournot duopoly system to demonstrate that this system is Lyapunov stable at its unique nonzero fixed point (Cournot equilibrium point) when the unit costs of the Cournot double oligarchies satisfy certain conditions. Therefore, we conclude that the Cournot duopoly system is safe relative to both sensitivity and Devaney chaos. The robustness of our results are also verified by conducting numerical simulations in the Cournot duopoly game.

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30

Deng, Jian. "Stochastic Stability of Coupled Viscoelastic Systems Excited by Real Noise." Mathematical Problems in Engineering 2018 (June 28, 2018): 1–14. http://dx.doi.org/10.1155/2018/4725148.

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The moment stochastic stability and almost-sure stochastic stability of two-degree-of-freedom coupled viscoelastic systems, under the parametric excitation of a real noise, are investigated through the moment Lyapunov exponents and the largest Lyapunov exponent, respectively. The real noise is also called the Ornstein-Uhlenbeck stochastic process. For small damping and weak random fluctuation, the moment Lyapunov exponents are determined approximately by using the method of stochastic averaging and a formulated eigenvalue problem. The largest Lyapunov exponent is calculated through its relation with moment Lyapunov exponents. The stability index, the stability boundaries, and the critical excitation are obtained analytically. The effects of various parameters on the stochastic stability of the system are then discussed in detail. Monte Carlo simulation is carried out to verify the approximate results of moment Lyapunov exponents. As an application example, the stochastic stability of a flexural-torsional viscoelastic beam is studied.

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31

Bernstein, D. S., and S. P. Bhat. "Lyapunov Stability, Semistability, and Asymptotic Stability of Matrix Second-Order Systems." Journal of Mechanical Design 117, B (June 1, 1995): 145–53. http://dx.doi.org/10.1115/1.2836448.

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Necessary and sufficient conditions for Lyapunov stability, semistability and asymptotic stability of matrix second-order systems are given in terms of the coefficient matrices. Necessary and sufficient conditions for Lyapunov stability and instability in the absence of viscous damping are also given. These are used to derive several known stability and instability criteria as well as a few new ones. In addition, examples are given to illustrate the stability conditions.

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32

Bernstein, D. S., and S. P. Bhat. "Lyapunov Stability, Semistability, and Asymptotic Stability of Matrix Second-Order Systems." Journal of Vibration and Acoustics 117, B (June 1, 1995): 145–53. http://dx.doi.org/10.1115/1.2838656.

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Necessary and sufficient conditions for Lyapunov stability, semistability and asymptotic stability of matrix second-order systems are given in terms of the coefficient matrices. Necessary and sufficient conditions for Lyapunov stability and instability in the absence of viscous damping are also given. These are used to derive several known stability and instability criteria as well as a few new ones. In addition, examples are given to illustrate the stability conditions.

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33

Li, Haitao, and Yuzhen Wang. "Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks." SIAM Journal on Control and Optimization 55, no. 6 (January 2017): 3437–57. http://dx.doi.org/10.1137/16m1092581.

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34

Aniszewska, Dorota, and Marek Rybaczuk. "Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems." Nonlinear Dynamics 54, no. 4 (January 25, 2008): 345–54. http://dx.doi.org/10.1007/s11071-008-9333-7.

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35

Waldner, Franz, and Rainer Klages. "Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited." Chaos, Solitons & Fractals 45, no. 3 (March 2012): 325–40. http://dx.doi.org/10.1016/j.chaos.2011.12.014.

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36

KHASMINSKII, R., and G. N. MILSTEIN. "STABILITY OF GYROSCOPIC SYSTEMS UNDER SMALL RANDOM EXCITATIONS." Stochastics and Dynamics 04, no. 01 (March 2004): 107–33. http://dx.doi.org/10.1142/s0219493704000924.

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Gyroscopic systems with two degrees of freedom under small random perturbations are investigated by use of the stochastic averaging principle. It is proved that the principal term of the Lyapunov exponent for the original system coincides with the Lyapunov exponent for the averaged system. An explicit formula for the averaged Lyapunov exponent is derived. The averaged moment Lyapunov exponent is also considered. An example is given in which an unstable gyroscopical system is stabilized by noise of the Stratonovich type.

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37

Shao, Hua, Yuming Shi, and Hao Zhu. "Lyapunov Exponents, Sensitivity, and Stability for Non-Autonomous Discrete Systems." International Journal of Bifurcation and Chaos 28, no. 07 (June 30, 2018): 1850088. http://dx.doi.org/10.1142/s0218127418500888.

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This paper focuses on the relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong sensitivity at a point and in a set, Lyapunov stability, and exponential asymptotical stability. It is shown that the positive Lyapunov exponent at a point implies strong sensitivity for a class of non-autonomous discrete systems. Furthermore, the uniformly positive Lyapunov exponents in a totally invariant set imply strong sensitivity in this set under certain conditions. The negative Lyapunov exponent at a point implies exponential asymptotical stability for a class of non-autonomous discrete systems. The related existing results for autonomous discrete systems are generalized to non-autonomous discrete systems and their conditions are weakened. One example is provided for illustration.

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38

Olas, Andrzej. "Recursive Lyapunov Functions." Journal of Dynamic Systems, Measurement, and Control 111, no. 4 (December 1, 1989): 641–45. http://dx.doi.org/10.1115/1.3153107.

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The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0). The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.

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39

Arnoldo Morales, Carlos, and M. J. Pacifico. "Lyapunov stability of $\omega$-limit sets." Discrete & Continuous Dynamical Systems - A 8, no. 3 (2002): 671–74. http://dx.doi.org/10.3934/dcds.2002.8.671.

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40

Vághy, Mihály A., and Gábor Szederkényi. "Lyapunov stability of generalized ribosome flows*." IFAC-PapersOnLine 55, no. 18 (2022): 56–61. http://dx.doi.org/10.1016/j.ifacol.2022.08.030.

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41

Naser, Mohammad Fuad Mohammad. "Nonsmooth Lyapunov stability of differential equations." Applied Mathematical Sciences 11 (2017): 887–95. http://dx.doi.org/10.12988/ams.2017.7277.

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42

Vaidya, Umesh, and Prashant G. Mehta. "Lyapunov Measure for Almost Everywhere Stability." IEEE Transactions on Automatic Control 53, no. 1 (February 2008): 307–23. http://dx.doi.org/10.1109/tac.2007.914955.

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43

Li, Z. "Lyapunov stability of discontinuous dynamic systems." IMA Journal of Mathematical Control and Information 16, no. 3 (September 1, 1999): 261–74. http://dx.doi.org/10.1093/imamci/16.3.261.

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44

Petrov, Alexey A., and Sergei Yu Pilyugin. "Lyapunov functions, shadowing and topological stability." Topological Methods in Nonlinear Analysis 43, no. 1 (April 12, 2016): 231. http://dx.doi.org/10.12775/tmna.2014.013.

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45

Florchinger, Patrick. "Lyapunov-Like Techniques for Stochastic Stability." SIAM Journal on Control and Optimization 33, no. 4 (July 1995): 1151–69. http://dx.doi.org/10.1137/s0363012993252309.

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46

Barron, E. N., and R. Jensen. "Lyapunov stability using minimum distance control." Nonlinear Analysis: Theory, Methods & Applications 43, no. 7 (March 2001): 923–36. http://dx.doi.org/10.1016/s0362-546x(99)00249-7.

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47

Stotsky, Alexander. "Stability of Traffic Flow: Lyapunov Analysis." IFAC Proceedings Volumes 30, no. 8 (June 1997): 759–64. http://dx.doi.org/10.1016/s1474-6670(17)43913-9.

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48

Iggidr, A., B. Kalitine, and R. Outbib. "Semidefinite lyapunov functions stability and stabilization." Mathematics of Control, Signals, and Systems 9, no. 2 (June 1996): 95–106. http://dx.doi.org/10.1007/bf01211748.

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49

Shevitz, D., and B. Paden. "Lyapunov stability theory of nonsmooth systems." IEEE Transactions on Automatic Control 39, no. 9 (1994): 1910–14. http://dx.doi.org/10.1109/9.317122.

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Rajaram, Rajeev, and Umesh Vaidya. "Robust stability analysis using Lyapunov density." International Journal of Control 86, no. 6 (June 2013): 1077–85. http://dx.doi.org/10.1080/00207179.2013.774463.

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