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
The asymptotic stability and exponential stability of nonlinear stochastic differential systems with Markovian switching and with polynomial growth
TL;DR: In this article, the authors discuss the asymptotic stability and exponential stability of nonlinear stochastic differential systems with Markovian switching (SDSwMSs), where the system coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition.
Journal ArticleDOI
Original article: L2-L∞ fuzzy control for Markov jump systems with neutral time-delays
Shuping He,Shuping He,Fei Liu +2 more
TL;DR: The L"2-L"~ fuzzy control problem is considered for nonlinear stochastic Markov jump systems with neutral time-delays and by means of Takagi-Sugeno fuzzy models, the fuzzy controller systems and the overall closed-loop fuzzy dynamics are constructed.
Journal ArticleDOI
Moment stability of discontinuous stochastic dynamical systems
Ling Hou,Anthony N. Michel +1 more
TL;DR: New Lyapunov and Lagrange stability results in the pth mean are established for a class of discontinuous stochastic dynamical systems and applied in the qualitative analysis of aclass of digital feedback control systems that are subjected to multiplicative and additive disturbances in the plants.
Proceedings ArticleDOI
Stability Analysis and Stabilization of Randomly Switched Systems
TL;DR: Stability analysis and stabilization of randomly switched systems with control inputs as a jump stochastic process and universal formulae for feedback stabilization of nonlinear systems for the corresponding control spaces constitute the primary tools for control design.
Proceedings ArticleDOI
Stability of linear Markovian jump systems
Xiangbo Feng,Kenneth A. Loparo +1 more
TL;DR: In this paper, the stability properties of linear Markovian jump systems and the relationship among second moment and sample path stability properties were studied. Butler et al. showed that asymptotic mean square stability, exponential mean square and stochastic stability are equivalent, and that they imply almost sure stability of the system.
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.