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
Further Results on Stability Analysis for Markovian Jump Systems with Time-Varying Delays
TL;DR: In this article, an improved delay-dependent stability criterion for Markovian jump systems with time-varying delays was proposed. But the proposed criterion is based on linear matrix inequalities (LMIs).
Journal ArticleDOI
Optimal inventory-production control problem with stochastic demand
TL;DR: In this article, the inventory-production control problem is formulated as a jump linear quadratic control problem and the optimal policy is obtained in terms of a set of coupled Riccati equations.
Mean square exponential stability for discrete-time time-varying linear systems with Markovian switching
Vasile Dragan,Toader Morozan +1 more
TL;DR: In this article, the problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to Markovian switching is investigated and four different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent.
Approximate Stochastic Optimal Control of Smooth Nonlinear Systems and Piecewise Linear Systems
TL;DR: In this paper, the authors propose a method to solve the problem of "missing links" in the literature.XIII, V.XII, and V.VIII.
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.
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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.