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
H ∞ -control for Markovian jumping linear systems with parametric uncertainty
Peng Shi,E. K. Boukas +1 more
TL;DR: In this article, the authors studied the problem of H∞-control for linear systems with Markovian jumping parameters and parameter uncertainties, where the jumping rates were assumed to be real, time-varying, norm-bounded, appearing in the state matrix.
Journal ArticleDOI
A survey on Markovian jump systems: Modeling and design
Peng Shi,Peng Shi,Fanbiao Li +2 more
TL;DR: In this paper, a survey on recent developments of modeling, analysis and design of Markovian jump systems is presented, and a variety of control and filter design methods are systematically recalled.
Journal ArticleDOI
Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems
TL;DR: The main contribution of the note is to provide a method for designing an asymptotically stable linear time-invariant Hinfin filter for systems where the jumping parameter is not accessible.
Journal ArticleDOI
On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters
TL;DR: This work focuses on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay.
Journal ArticleDOI
Stability analysis for stochastic hybrid systems
TL;DR: This survey addresses stability analysis for stochastic hybrid systems (SHS) by reviewing many of the stability concepts that have been studied, including Lyapunov stability, Lagrange stability, asymptotic stability, and recurrence.
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.