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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Robust Kalman filter of discrete-time Markovian jump system with parameter and noise uncertainty
TL;DR: In this paper, robust Kalman filtering problems for discrete-time Markovian jump systems with parameter and noise uncertainty were investigated, and the maximum admissible upper bound of the disturbance to noise covariance matrix was given based on the estimation performance.
Proceedings ArticleDOI
Observer Design with Guaranteed RMS Gain for Linear Parameter Varying Jump Systems
TL;DR: It is shown in the paper that an upper bound on the RMS gain of the observer can be characterized in terms of robust feasibility of a family of linear matrix inequalities (LMIs) that can be used to explicitly construct a parameter-varying jump observer that guarantees the desired performance level.
Journal ArticleDOI
Sliding Mode State Feedback Control for Uncertain Discrete-Time Markov Jump Systems*
TL;DR: In this paper, a state feedback sliding mode controller for uncertain discrete-time Markov jump systems is proposed, and a sufficient condition is provided to guarantee the existence of the discrete time sliding modes in an LMI form.
Journal ArticleDOI
Robust Control for Linear Systems with Markovian Jumping Parameters
El-Kébir Boukas,K. Benjelloun +1 more
TL;DR: In this paper, the robustness of linear systems with markovian jumping parameters with matched and mismatched uncertainties was investigated and a sufficient condition for stochastic stabilizability of this class of systems was established.
Proceedings ArticleDOI
Exact statistical moments of multi-mode stochastic hybrid systems with renewal transitions
TL;DR: This paper studies how random switching of a gene between transcriptionally active and inactive states drives stochastic variation in the level of the expressed protein, and presents a novel method to derive exact analytical solutions for the statistical moments.
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.