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
Stochastic stabilizability and H∞ control for markovian jump time-delay systems
Yong-Yan Cao,James Lam +1 more
TL;DR: In this paper, the stochastic stabilizability and H ∞ disturbance attenuation for linear time-delay systems that possess randomly jumping parameters are investigated, where the transition of the jumping parameters is governed by a finite-state Markov process.
Posted Content
Linear piecewise-deterministic Markov processes with families of random discrete events
Mohammad Soltani,Abhyudai Singh +1 more
TL;DR: In this article, the authors consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system and provide explicit conditions that lead to finite stationary moments, and corresponding exact closed-form moment formulas.
Journal ArticleDOI
Stability Optimization of Positive Semi-Markov Jump Linear Systems via Convex Optimization
TL;DR: The stability optimization problem reduces to a convex optimization problem under certain regularity conditions on the system matrices and the cost function by using a result from the matrix theory on the log-log convexity of the spectral radius of nonnegative matrices.
Journal ArticleDOI
ℋ2 and ℋ∞ Filtering for Continuous-Time Markov Jump Lur'e Systems with Sector Bound Optimization
TL;DR: In this paper , the authors consider the filtering of Markov jump systems subject to a class of nonlinearities which include them on the Lur'e systems framework and present strategies which allow them to design either mode-dependent and modeindependent filters, with sector bound optimisation.
Journal ArticleDOI
Robust control under constraints of linear systems with Markovian jumps
TL;DR: In this paper, the robustness of continuous-time linear systems with Markovian jumps (LSMJ) and saturated input is studied. But the authors focus on the linear state feedback controller.
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.