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
Robust L2-L∞ Controller Design of a Class of Uncertain Stochastic Systems with Wiener Process Disturbances
TL;DR: The optimal L2-L∞ control problem of a class of uncertain stochastic systems with Wiener process disturbances is studied and based on the robust L 2-L ∞ control theory, it gives a sufficient condition for optimal control of these systems.
Proceedings ArticleDOI
Topological formulation of discrete-time switched linear systems and almost sure stability
TL;DR: It is shown that the approach captures the maximal set of stable processes for linear switched systems, where the measure is the natural Markov measure defined by the transition probability matrix.
Journal ArticleDOI
Mean escape time of switched Riccati differential equations
Masaki Ogura,Clyde F. Martin +1 more
TL;DR: In this article , the authors analyzed the mean escape time of a Riccati differential equation driven by a Poisson-like stochastic signal and showed that it admits a power series expression.
Journal ArticleDOI
Linear-quadratic stochastic leader-follower differential games for Markov jump-diffusion models
TL;DR: In this article , the authors considered the linear-quadratic leader-follower Stackelberg differential game with Markov jump-diffusion stochastic differential equations (SDEs).
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.