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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Book ChapterDOI
Stochastic robust stability analysis for markovian jump discrete-time delayed neural networks with multiplicative nonlinear perturbations
TL;DR: The problem of stochastic robust stability for Markovian jump discrete-time delayed neural networks with multiplicative nonlinear perturbation is investigated via Lyapunov stability theory through a novel analysis approach based on the linear matrix inequality (LMI) methodology.
Proceedings ArticleDOI
Energy-to-peak filtering for Markov jump systems
TL;DR: In this paper, the energy-to-peak filtering problem of Markov jump systems is investigated and the existence condition and design method for filter are presented to achieve a prespecified peak level of estimation error against all bounded energy noises.
With markovian jumping parameters
TL;DR: A necessary and L,yapunov exponent for the DTLSMJP in terms of a set of coupled discrete-time algebraic Riccati eaquations is given in this paper.
Proceedings Article
Delay-dependent passive control for stochastic differential systems with Markov switching and time delay
TL;DR: In this paper, a new conception of passivity is presented, and the condition for delay-dependent passiveness of such stochastic systems is obtained by constructing a new type of Lyapunov-Krasovskii function, employing model transformation and Newton-Leibniz equality and slack matrix technique.
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.