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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Proceedings ArticleDOI
Almost sure Stability of Stochastic Switched Systems: Graph lifts-based Approach
TL;DR: This paper provides a characterization of almost sure stability of stochastic switched systems whose switching signal is constrained by an automaton in terms of multiple Lyapunov functions, and introduces the concept of lifts, providing formal expansions of Stochastic graphs, together with the guarantee of conserving the underlying probability framework.
Proceedings Article
Filter design of delayed nonlinear discrete-time Markovian neural networks systems with missing measurements
TL;DR: In this article, a L2-L∞ filtering scheme for nonlinear discrete-time Markovian jumping neural networks with time delay under missing output measurements is presented, and the gain matrix of the filter can be derived from the solution of a set of linear matrix inequalities.
Book ChapterDOI
Robust H ∞ Fuzzy Control Design for Nonlinear Two-Time Scale System with Markovian Jumps based on LMI Approach
TL;DR: In this article, a robust H1 state-feedback controller for a class of nonlinear two-time scale systems with Markovian jumps described by a Takagi-Sugeno (TS) fuzzy model is presented.
Proceedings Article
Delay-range-dependent robust output-feedback stabilization for Markovian jump systems with mode-dependent time delays and nonliearities
Yi Zhang,Qingling Zhang +1 more
TL;DR: In this paper, the authors considered the exponential mean-square stabilization problem via dynamic output-feedback controller for Markovian jump systems with nonlinear perturbations and time delays.
Delay-range-dependenth∞ control for markovian jump systems with mode-dependent time delays
TL;DR: In this paper, the authors considered mean-square exponential stability and H∞ control problems for Markovian jump systems (MJSs) with time delays which are time-varying in an interval and depend on system mode.
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.