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
Robust finite-time estimation of Markovian jumping systems with bounded transition probabilities
Shuping He,Fei Liu +1 more
TL;DR: In terms of linear matrix inequalities (LMIs) techniques, the sufficient condition on the existence of finite-time H"~ filter is presented and proved and the filter matrices can be solved directly by using the existing LMIs optimization techniques.
Journal ArticleDOI
Stabilisation of stochastic systems with optimal decay rate
TL;DR: In this paper, the authors deal with the problem of exponential stabilisation for continuous-time stochastic systems and present several equivalent characterisations for exponential stability of continuous time systems.
Journal ArticleDOI
Randomized Algorithms for Robust Stability and Guaranteed Cost Control of Stochastic Jump Parameter Systems with Uncertain Switching Policies
TL;DR: In this paper, uncertainty randomization is applied to robust control of stochastic systems governed by uncertain discrete-state Markov processes, and new possibilities which this approach may offer in relation to robust stability and control are investigated.
Book ChapterDOI
Stochastic robust stability analysis for Markovian jumping neural networks with time delays
TL;DR: A novel approach for stability analysis of neural networks is developed based on Lyapunov stability theory, and the sufficient conditions of stochastic robust stability are given in terms of linear matrix inequalities (LMIs).
Journal ArticleDOI
Simultaneous ℋ︁2/ℋ︁∞ control of uncertain jump systems with functional time‐delays
TL;DR: In this article, the authors present new results pertaining to the control design of a class of linear uncertain systems with Markovian jump parameters, where an integral part of the system dynamics is a delayed state in which the time-delays are mode dependent.
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.