Journal ArticleDOI
Stochastic stability properties of jump linear systems
TLDR
In this paper, the authors studied stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties, and showed that all second moment stability properties are equivalent and are sufficient for almost sure sample path stabilisation.Abstract:
Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/. >read more
Citations
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Journal ArticleDOI
A sufficient condition for stability of a polytope of matrices
TL;DR: In this article, a sufficient condition for the stability of a polytope of matrices, which is shown to be necessary and sufficient for a certain class of matrix, is obtained.
Journal ArticleDOI
A Brief Tutorial and Survey on Markovian Jump Systems: Stability and Control
Ping Zhao,Yu Kang,Yun-Bo Zhao +2 more
TL;DR: Markovian jump systems are hybrid dynamic systems typically consisting of both the dynamic state space and the set of discrete events, where a Markov process describes the discrete events for MJSs.
Studies on Stability and Stabilization of Randomly Switched Systems
TL;DR: In this paper, the authors present a study on stability analysis and stabilizing controller synthesis of randomly switched systems, where a family of nonlinear subsystems and a random switching signal are used to specify which subsystem is active at each time instant.
Proceedings ArticleDOI
Independent delay sufficient conditions for robust stability of uncertain linear time-delay systems with jumps
TL;DR: Under the assumption of complete access to the continuous state and the boundedness of the system's uncertainties, an independent delay sufficient conditions which guarantee the robustness stability of this class of systems are established.
Journal ArticleDOI
On almost sure stability conditions of linear switching stochastic differential systems
TL;DR: In this paper, the authors consider the systems affected by Poisson process and Wiener process and investigate their joint effects on stability, and derive the almost sure stability conditions by using some fundamental convergence theorem.
References
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Book
Stochastic Stability and Control
TL;DR: In this article, a book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes is presented, which is based on the work of this article.
Journal ArticleDOI
Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control
Y. Ji,Howard J. Chizeck +1 more
TL;DR: In this paper, necessary and sufficient conditions for the existence of finite cost, constant, stabilizing controls for the infinite-time Markovian jump linear quadratic (JLQ) problem are established.
Random differential equations in control theory
TL;DR: In this article, the authors discuss control processes and optimization problems solutions by stochastic differential equations, discussing dynamic models and programming, linear filtering and optimal feedback, and discuss linear filtering with optimal feedback.
Journal ArticleDOI
A survey of stability of stochastic systems
TL;DR: The main purpose of this manuscript is to give some understanding of the subject of stability of stochastic systems by presenting some of the basic ideas as well as a survey of results that have appeared in the literature.
Journal ArticleDOI
Feedback control of a class of linear systems with jump parameters
TL;DR: In this paper, a class of linear systems are studied which are subject to sudden changes in parameter values and an algorithm similar in form to Kushner's stochastic maximum principle is derived.