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
Observer-based finite-time control of time-delayed jump systems
Shuping He,Fei Liu +1 more
TL;DR: Substantial conditions that ensure stochastic robust control performance of time-delay jump systems are derived and the designed finite-time stabilization controller is described as an optimization one and is extended to time-varying delayed MJSs.
Journal ArticleDOI
Fuzzy model‐based fault detection for Markov jump systems
Shuping He,Fei Liu +1 more
TL;DR: In this paper, the robust fault detection filter (RFDF) design problems for nonlinear stochastic time-delay Markov jump systems were studied by means of the Takagi-Sugeno fuzzy models, the fuzzy RFDF system and the dynamics of filtering error generator were constructed.
Journal ArticleDOI
Almost Sure Stabilization of Uncertain Continuous-Time Markov Jump Linear Systems
TL;DR: A deterministically testable sufficient condition for robust AS stability is provided which relies on a bound on the 2-norm of the system transition matrix which can be profitably employed also to design a robust feedback stabilization strategy.
Journal ArticleDOI
Stabilization of Markovian Systems via Probability Rate Synthesis and Output Feedback
Jun-e Feng,James Lam,Zhan Shu +2 more
TL;DR: A novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of Markovian jump linear systems.
Journal ArticleDOI
Master-Slave Global Stochastic Synchronization of Chaotic Oscillators
TL;DR: Stochastic Lyapunov stability theory and partial averaging techniques are used to show that global synchronization is possible if the switching period is sufficiently small and if the oscillators globally synchronize under a time-averaged coupling.
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.