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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Proceedings ArticleDOI
Approximation methods for optimal network coding in a multi-hop control network with packet losses
TL;DR: This paper proposes an approximation that takes into account both the network parameters and the system dynamics: it is based on the assumption that packet loss probabilities are much smaller than correct transmission probabilities and leverages the well known Gerschgorin disks.
Journal ArticleDOI
On an infinite dimensional perturbed Riccati differential equation arising in stochastic control
TL;DR: In this paper, the existence and uniqueness of solutions for a class of infinite dimensional perturbed Riccati differential equations in a certain Banach space is studied, which arises in control problems involving linear systems with countably infinite Markov jump parameters.
Journal ArticleDOI
Robust finite-time H∞ control of stochastic jump systems
Shuping He,Fei Liu +1 more
TL;DR: In this paper, the stochastic finite-time stabilization and H∞ control problem of Mar-Kov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters is provided.
Proceedings ArticleDOI
Stability of nonlinear asynchronous systems
TL;DR: This work studies the behavior of this class of nonlinear asynchronous systems defined by two different modes of operation, one stable and the other one unstable, and provides existential results of conditions on this rate constraint under which various types of stability of the origin of the non linear asynchronous system can be assured.
Proceedings ArticleDOI
Stochastic stability of fault tolerant control systems in the presence of noise
TL;DR: In this paper, the stochastic stability of fault tolerant control systems (FTCS) in the presence of white Gaussian noise is studied using the Lyapunov function approach, and it is shown that the exponential stability in the mean square is sufficient for almost sure asymptotic stability.
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.