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Relevant bibliographies by topics / Differential Lyapunov equations

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Academic literature on the topic 'Differential Lyapunov equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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Journal articles on the topic "Differential Lyapunov equations"

1

Barreira, Luis, and Claudia Valls. "Regularity Coefficients for Impulsive Differential Equations." Quarterly Journal of Mathematics 71, no. 4 (2020): 1535–56. http://dx.doi.org/10.1093/qmath/haaa048.

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Abstract For a linear impulsive differential equation, we introduce a Lyapunov regularity coefficient following as far as possible the non-impulsive case. We recall that a regularity coefficient is a quantity that characterizes the Lyapunov regularity of the dynamics. In particular, we obtain lower and upper bounds for the Lyapunov regularity coefficient and we show that its computation can always be reduced to that of the corresponding coefficient of an impulsive dynamics defined by upper triangular matrices. We also relate the Lyapunov regularity coefficient with the Grobman regularity coeff

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2

Burton, T. A. "Fractional differential equations and Lyapunov functionals." Nonlinear Analysis: Theory, Methods & Applications 74, no. 16 (2011): 5648–62. http://dx.doi.org/10.1016/j.na.2011.05.050.

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Berger, B. S., and M. Rokni. "Lyapunov exponents for discontinuous differential equations." Quarterly of Applied Mathematics 48, no. 3 (1990): 549–53. http://dx.doi.org/10.1090/qam/1074970.

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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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Cañada, Antonio, Juan A. Montero, and Salvador Villegas. "Lyapunov-type Inequalities for Differential Equations." Mediterranean Journal of Mathematics 3, no. 2 (2006): 177–87. http://dx.doi.org/10.1007/s00009-006-0071-0.

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Barreira, Luis, and Claudia Valls. "Lyapunov regularity of impulsive differential equations." Journal of Differential Equations 249, no. 7 (2010): 1596–619. http://dx.doi.org/10.1016/j.jde.2010.07.016.

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7

Cañada, A., J. A. Montero, and S. Villegas. "Lyapunov inequalities for partial differential equations." Journal of Functional Analysis 237, no. 1 (2006): 176–93. http://dx.doi.org/10.1016/j.jfa.2005.12.011.

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CONG, NGUYEN DINH. "LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 01, no. 01 (2001): 127–57. http://dx.doi.org/10.1142/s0219493701000084.

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We introduce a concept of Lyapunov exponents and Lyapunov spectrum for nonautonomous linear stochastic differential equations. The Lyapunov exponents are defined samplewise via the two-parameter flow generated by the equation. We prove that Lyapunov exponents are finite and nonrandom. Lyapunov exponents are used for investigation of Lyapunov regularity and stability of nonautonomous stochastic differential equations. The results show that the concept of Lyapunov exponents is still very fruitful for stochastic objects and gives us a useful tool for investigating sample stability as well as qual

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9

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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Cong, Nguyen Dinh, Luu Hoang Duc, and Phan Thanh Hong. "Lyapunov Spectrum of Nonautonomous Linear Young Differential Equations." Journal of Dynamics and Differential Equations 32, no. 4 (2019): 1749–77. http://dx.doi.org/10.1007/s10884-019-09780-z.

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Abstract We show that a linear Young differential equation generates a topological two-parameter flow, thus the notions of Lyapunov exponents and Lyapunov spectrum are well-defined. The spectrum can be computed using the discretized flow and is independent of the driving path for triangular systems which are regular in the sense of Lyapunov. In the stochastic setting, the system generates a stochastic two-parameter flow which satisfies the integrability condition, hence the Lyapunov exponents are random variables of finite moments. Finally, we prove a Millionshchikov theorem stating that almos

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Dissertations / Theses on the topic "Differential Lyapunov equations"

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Siegert, Wolfgang. "Local Lyapunov exponents sublimiting growth rates of linear random differential equations." Berlin Heidelberg Springer, 2007. http://d-nb.info/991321065/04.

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2

Zhang, Xiling. "On numerical approximations for stochastic differential equations." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28931.

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This thesis consists of several problems concerning numerical approximations for stochastic differential equations, and is divided into three parts. The first one is on the integrability and asymptotic stability with respect to a certain class of Lyapunov functions, and the preservation of the comparison theorem for the explicit numerical schemes. In general, those properties of the original equation can be lost after discretisation, but it will be shown that by some suitable modification of the Euler scheme they can be preserved to some extent while keeping the strong convergence rate maintai

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Ogundare, Babatunde Sunday. "Qualitative and quantitative properties of solutions of ordinary differential equations." Thesis, University of Fort Hare, 2009. http://hdl.handle.net/10353/244.

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This thesis is concerned with the qualitative and quantitative properties of solutions of certain classes of ordinary di erential equations (ODEs); in particular linear boundary value problems of second order ODE's and non-linear ODEs of order at most four. The Lyapunov's second method of special functions called Lyapunov functions are employed extensively in this thesis. We construct suitable complete Lyapunov functions to discuss the qualitative properties of solutions to certain classes of non-linear ordinary di erential equations considered. Though there is no unique way of constructing Ly

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Siegert, Wolfgang [Verfasser]. "Local Lyapunov exponents : sublimiting growth rates of linear random differential equations / Wolfgang Siegert." Berlin, 2008. http://d-nb.info/992547660/34.

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Kuhn, Zuzana. "Ranges of vector measures and valuations." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/30875.

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Arugaslan, Cincin Duygu. "Differential Equations With Discontinuities And Population Dynamics." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12610574/index.pdf.

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In this thesis, both theoretical and application oriented results are obtained for differential equations with discontinuities of different types: impulsive differential equations, differential equations with piecewise constant argument of generalized type and differential equations with discontinuous right-hand sides. Several qualitative problems such as stability, Hopf bifurcation, center manifold reduction, permanence and persistence are addressed for these equations and also for Lotka-Volterra predator-prey models with variable time of impulses, ratio-dependent predator-prey systems and lo

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Herzog, David Paul. "Geometry's Fundamental Role in the Stability of Stochastic Differential Equations." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145150.

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We study dynamical systems in the complex plane under the effect of constant noise. We show for a wide class of polynomial equations that the ergodic property is valid in the associated stochastic perturbation if and only if the noise added is in the direction transversal to all unstable trajectories of the deterministic system. This has the interpretation that noise in the "right" direction prevents the process from being unstable: a fundamental, but not well-understood, geometric principle which seems to underlie many other similar equations. The result is proven by using Lyapunov functio

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Thai, Son Doan. "Lyapunov Exponents for Random Dynamical Systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-25314.

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In this thesis the Lyapunov exponents of random dynamical systems are presented and investigated. The main results are: 1. In the space of all unbounded linear cocycles satisfying a certain integrability condition, we construct an open set of linear cocycles have simple Lyapunov spectrum and no exponential separation. Thus, unlike the bounded case, the exponential separation property is nongeneric in the space of unbounded cocycles. 2. The multiplicative ergodic theorem is established for random difference equations as well as random differential equations with random delay. 3. We provide a co

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Safi, Mohammed. "Stabilité de Lyapunov de systèmes couplés impliquant une équation de transport." Thesis, Toulouse, ISAE, 2018. http://www.theses.fr/2018ESAE0022/document.

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L’objet de cette thèse est l’étude des propriétés de stabilité et contrôle pour des systèmes linéaires écrits à l’aide d’équations aux dérivées partielles (EDP) ou d’équations à retard. Nous souhaitons exploiter dans cette thèse les liens qui existent entre ces deux classes de systèmes de dimension infinie afin de développer une nouvelle approche permettant leur analyse. En effet dans plusieurs applications, il est possible de choisir l’un ou l’autre de ces deux types de systèmes pour modéliser la dynamique considérée. Par exemple, les phénomènes de congestion dans un réseau routier peuvent êt

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Garcia, Lucas Felipe Rodrigues dos Santos. "Estabilidade para equações diferenciais em medida." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-01042008-110225/.

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Neste trabalho, nós investigamos a estabilidade da solução trivial da seguinte Equação Diferencial em Medida (EDM) Dx = f(x, t) + g(x, t)Du, (1) onde \'B BARRA IND. c\' = {\'x PERTENCE A\' \'R POT. n\'; //x// \' < OU=\' c}, f : \'B BARRA IND.c\' × [a, b] \'SETA\' \'R POT.n\' e g : \'B BARRA IND. c\' × [a, b] \'SETA\' \' R POT n\', u : [a, b] \' ETA\' ! R é uma função de variação limitada em [a, b] e contínua à esquerda em (a, b], f(x, ·) é Lebesgue integrável em [a, b], g(x, ·) é du-integrável em [a, b], f(0, t) = 0 = g(0, t) para todo t e Dx e Du denotam as derivadas distribucionais de

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Books on the topic "Differential Lyapunov equations"

1

Izobov, N. A. Lyapunov exponents and stability. CSP/Cambridge Scientific Publishers, 2012.

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2

Claudia, Valls, ed. Stability of nonautonomous differential equations. Springer, 2008.

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3

Shaĭkhet, L. E. Lyapunov functionals and stability of stochastic difference equations. Springer, 2011.

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4

Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer International Publishing, 2013.

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Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00101-2.

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A, Mitropolʹskiĭ I͡U. Issledovanii͡a dikhotomii lineĭnykh sistem different͡sialʹnykh uravneniĭ s pomoshchʹi͡u funkt͡siĭ Li͡apunova. Nauk. dumka, 1990.

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7

Orlik, Lyubov', and Galina Zhukova. Operator equation and related questions of stability of differential equations. INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1061676.

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The monograph is devoted to the application of methods of functional analysis to the problems of qualitative theory of differential equations. Describes an algorithm to bring the differential boundary value problem to an operator equation. The research of solutions to operator equations of special kind in the spaces polutoratonny with a cone, where the limitations of the elements of these spaces is understood as the comparability them with a fixed scale element of exponential type. Found representations of the solutions of operator equations in the form of contour integrals, theorems of existe

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8

M, Matrosov V., and Sivasundaram S, eds. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems. Springer Netherlands, 1991.

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9

Mazanik, S. A. Preobrazovanii︠a︡ li︠a︡punova lineĭnykh different︠s︡ialʹnykh sistem. BGU, 2008.

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10

Stability analysis of impulsive functional differential equations. Walter de Gruyter, 2009.

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Book chapters on the topic "Differential Lyapunov equations"

1

Barreira, Luís. "Linear Differential Equations." In Lyapunov Exponents. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71261-1_4.

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2

Kim, A. V. "The Lyapunov Functional Method." In Functional Differential Equations. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-1630-7_7.

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Kim, A. V. "The Lyapunov Function Method." In Functional Differential Equations. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-1630-7_8.

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4

Jleli, Mohamed, Mokhtar Kirane, and Bessem Samet. "Lyapunov-type inequalities for fractional boundary value problems." In Fractional Differential Equations, edited by Anatoly Kochubei and Yuri Luchko. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571660-006.

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Agarwal, Ravi P., Martin Bohner, and Abdullah Özbekler. "Lyapunov-Type Inequalities for Partial Differential Equations." In Lyapunov Inequalities and Applications. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69029-8_6.

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Agarwal, Ravi P., Martin Bohner, and Abdullah Özbekler. "Lyapunov-Type Inequalities for Fractional Differential Equations." In Lyapunov Inequalities and Applications. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69029-8_5.

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7

Boichenko, Vladimir A., Gennadij A. Leonov, and Volker Reitmann. "Dimension and Lyapunov functions." In Dimension Theory for Ordinary Differential Equations. Vieweg+Teubner Verlag, 2005. http://dx.doi.org/10.1007/978-3-322-80055-8_4.

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Barreira, Luis, and Yakov Pesin. "Lyapunov stability theory of differential equations." In Lyapunov Exponents and Smooth Ergodic Theory. American Mathematical Society, 2001. http://dx.doi.org/10.1090/ulect/023/02.

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Agarwal, Ravi P., Martin Bohner, and Abdullah Özbekler. "Lyapunov-Type Inequalities for Half-Linear Differential Equations." In Lyapunov Inequalities and Applications. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69029-8_3.

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Jones, John. "Matrix Differential Equations and Lyapunov Transformations." In Advances in Optimization and Control. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-46629-8_1.

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Conference papers on the topic "Differential Lyapunov equations"

1

Chiu H. Choi. "Solving stiff Lyapunov differential equations." In Proceedings of 2000 American Control Conference (ACC 2000). IEEE, 2000. http://dx.doi.org/10.1109/acc.2000.879191.

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Giesl, Peter, Carlos Argáez, Sigurdur Hafstein, and Holger Wendland. "Construction of a Complete Lyapunov Function using Quadratic Programming." In Special Session on Control Theory and Differential Equations. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0006944305600568.

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Björnsson, Hjörtur, Peter Giesl, Skuli Gudmundsson, and Sigurdur Hafstein. "Local Lyapunov Functions for Nonlinear Stochastic Differential Equations by Linearization." In Special Session on Control Theory and Differential Equations. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0006944505790586.

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Nishimura, Yuki. "Stochastic Lyapunov Stability for Rough Differential Equations." In 2019 18th European Control Conference (ECC). IEEE, 2019. http://dx.doi.org/10.23919/ecc.2019.8796199.

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SIMÓ, CARLES. "ON THE USE OF LYAPUNOV EXPONENTS TO DETECT GLOBAL PROPERTIES OF THE DYNAMICS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0105.

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Keqin Gu and Yi Liu. "Lyapunov-Krasovskii functional for coupled differential-functional equations." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434249.

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Giesl, Peter, and Najla Mohammed. "Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions." In Special Session on Control Theory and Differential Equations. SCITEPRESS - Science and Technology Publications, 2018. http://dx.doi.org/10.5220/0006944405690578.

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Leonov, G. A., and S. M. Seledzhi. "Lyapunov Dimension of Attractors of the Lorenz-Like Differential Equations." In 2016 Third International Conference on Mathematics and Computers in Sciences and in Industry (MCSI). IEEE, 2016. http://dx.doi.org/10.1109/mcsi.2016.032.

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Prieur, Christophe, and Frederic Mazenc. "ISS Lyapunov functions for time-varying hyperbolic partial differential equations." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6160401.

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Gillis, Joris, and Moritz Diehl. "A positive definiteness preserving discretization method for Lyapunov differential equations." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6761121.

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