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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Stochastic stability, passivity analysis and synthesis of markovian jump systems of neutral type
Xuyang Lou,Baotong Cui +1 more
TL;DR: In this paper, a sufficient condition on passivity for the solvability of a Markovian jump system with state time-varying delay is proposed, where the passive controller via memoryless statefeedback is given to guarantee the stability and passivity of appropriate closed-loop systems.
Proceedings Article
Neural Network-Based H infinity Filtering for Nonlinear Jump Systems.
Xiao-Li Luan,Fei Liu +1 more
TL;DR: A neural network-based Markovian H∞filter is developed using the stochastic Lyapunov-Krasovskii stability theory under some linear matrix inequality (LMI) constraints to show the usefulness of theoretical results.
Proceedings ArticleDOI
Stabilization of cluster in wireless sensor and actor network
TL;DR: Using theories of jump linear system, mode-independent and mode-dependent controllers satisfying mean square stability are successfully designed for stabilization of multi-sensor and single controller system with long but bounded multiple random time-delay and packet-loss.
Proceedings ArticleDOI
Hybrid system with Markov switching
TL;DR: In this paper, a new hybrid system was introduced, where the dynamical behavior of the discrete state is a Markov chain, and the properties of the Markov Chain were discussed.
Estabilidade estocástica de sistemas lineares com Saltos Markovianos e Sistemas Lineares com Saltos Semimarkovianos
TL;DR: In this paper, the second moment τ -stability of a continuous-time Markov jump linear system with infinite-time horizon was studied. And the authors showed that τ-stability is a sufficient condition for stochastic stability.
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.