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
Further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems
Jian Zhang,Yungang Liu,Xiaowu Mu +2 more
TL;DR: It is turned out that, with the designed controller in loop, all the closed-loop system states are globally bounded and the original system states converge to the origin, both in the sense of probability one.
Journal ArticleDOI
Feedback Stabilization of Bernoulli Jump Nonlinear Systems: A Passivity-Based Approach
Yingbo Zhao,Vijay Gupta +1 more
TL;DR: A state feedback controller that stabilizes a wide class of Bernoulli jump nonlinear systems is designed using passivity-based tools and the advantage is that the nonlinear dynamics can be non-affine in the control input.
Journal ArticleDOI
A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States
Qiang Ling,Haojiang Deng +1 more
TL;DR: The proof in this paper demonstrates well the essential properties of the Markov jump systems and achieves the desired result in the real state space.
Proceedings ArticleDOI
Bounded real lemma for nonhomogeneous Markovian jump linear systems
TL;DR: A bounded real lemma is established for discrete-time Markov jump linear systems with nonhomogeneous finite state Markov chain with different cases of arbitrary variation and periodic variation.
Proceedings ArticleDOI
Robust stability and stabilization of discrete-time Markov jump linear systems with partly unknown transition probability matrix
TL;DR: An improved linear matrix inequality (LMI) approach is proposed to deal with the problems of stability, mode-dependent and mode-independent stabilization of discrete-time Markov jump linear systems (MJLS) with partly unknown transition probability matrix, providing less conservative results when compared to other conditions available in the literature.
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.