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 -∞ Filtering of Time-Delay Jump Systems with Respect to the Finite-Time Interval
Shuping He,Fei Liu +1 more
TL;DR: In this article, the authors studied the problem of stochastic finite-time boundedness and disturbance attenuation for a class of linear time-delayed systems with Markov jumping parameters.
Proceedings ArticleDOI
Probabilistic robustness analysis of stochastic jump linear systems
TL;DR: In this paper, the authors proposed a new method to measure the probabilistic robustness of stochastic jump linear systems with respect to both the initial state uncertainties and the randomness in switching.
Journal ArticleDOI
Asymptotic stability in the distribution of nonlinear stochastic systems with semi-markovian switching
TL;DR: In this paper, the authors introduced finite phase semi-Markov processes, which can be transformed to a finite Markov chain, and obtained asymptotic stability for the distribution of nonlinear stochastic systems with semi-markovian switching.
Proceedings ArticleDOI
Stabilization of continuous-time nonlinear switched systems
TL;DR: In this article, a strategy for global stabilization of continuous time nonlinear switched systems is proposed, which is of closed loop nature and is designed from the solution of nonlinear Lyapunov-Metzler inequalities from which the stability condition is expressed.
Journal ArticleDOI
Stabilizing Sampled-data Linear Systems with Markovian Packet Losses and Random Sampling
TL;DR: In this paper, the stability properties and stabilizing problem of sampled-data networked controlled linear systems with Markovian packet losses were considered and necessary and sufficient conditions for the stochastic stability properties were established by using the known results of Markov jump linear systems and randomly sampled systems.
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.