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
Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control
Huai-Ning Wu,Kai-Yuan Cai +1 more
TL;DR: The aim is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system (MJFS) is robustly stochastically stable and derived for the uncertain MJFS in terms of linear matrix inequalities (LMIs).
Journal ArticleDOI
Stability and Stabilization of Discrete-Time Semi-Markov Jump Linear Systems via Semi-Markov Kernel Approach
TL;DR: A new stability concept generalizing the traditional mean-square stability is proposed such that numerically testable criteria on the basis of SMK are obtained.
Journal ArticleDOI
Sliding mode control for semi-Markovian jump systems via output feedback
TL;DR: A sliding mode controller is synthesized to drive the underlying closed-loop system onto the sliding surface in finite time, locally for a given sliding region, which also guarantees the stochastic stability of sliding mode dynamical system.
Journal ArticleDOI
Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems
TL;DR: It is proved that continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced always converge, and a sufficient condition is given on the evolving interaction topology for the limit values of two agents to be the same.
Journal ArticleDOI
Stochastic stability of jump linear systems
Yuguang Fang,Kenneth A. Loparo +1 more
TL;DR: Some testable conditions for mean square (i.e., second moment) stability for discrete-time jump linear systems with time-homogenous and time-inhomogenous finite state Markov chain form processes are presented.
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.