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
On the stabilization of switched linear stochastic systems with unobservable switching laws
Peng Ye,Haitao Fang +1 more
TL;DR: In this paper, it was shown that if each individual subsystem is controllable and the switching duration uniformly has a strict positive lower bound, then the system can be stabilized by using a controller that uses online state estimation.
Proceedings ArticleDOI
A Stabilizing Control Algorithm for Asynchronous Parallel Quadratic Programming via Dual Decomposition
TL;DR: A formal algorithm is provided to ensure the asymptotic stability of dual variables and it is shown that the implementation of the proposed algorithm guarantees the uniqueness of optimal solutions, irrespective of asynchronous behavior.
Journal ArticleDOI
Output tracking of Markovian jumping systems via error feedback regulation
TL;DR: With the extension of output regulation to MJSs, sufficient conditions are obtained based on stochastic Lyapunov-Krasovskii functional and the resulting closed-loop system is guaranteed to be stochastically stable and the output tracking is achieved almost asymptotically.
Proceedings ArticleDOI
Optimal control of time-varying fault tolerant systems
Adam Czornik,Andrzej Swierniak +1 more
TL;DR: An optimal control law for continuous infinite time-varying stochastic control systems with jumps and quadratic cost is found under assumption that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable.
Proceedings ArticleDOI
Stabilization of Discrete-time Linear Systems with Markov Switching in the Presence of Delays in Transmission of the Date
Vasile Dragan,T. Morozan +1 more
TL;DR: In this article, the authors investigate the problem of designing a stabilizing static output feedback gain for a discrete time linear system affected by a Markov chain in the presence of a possible delay in the transmission of the measurements.
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.