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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Strategies and Tactics in Multiscale Modeling of Cell-to-Organ Systems
TL;DR: The processes of error recognition, and of mapping between different levels of model complexity and shifting the levels of complexity of models in response to changing conditions, are essential for adaptive modeling and computer simulation of large-scale systems in reasonable time.
Journal ArticleDOI
Lyapunov coupled equations for continuous-time infinite Markov jump linear systems
TL;DR: In this article, it is shown that the Markov chain is stochastically stabilizable (SS) if and only if the associated countably infinite coupled Lyapunov equations have a unique norm bounded strictly positive solution.
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Consensus in Correlated Random Wireless Sensor Networks
TL;DR: It is shown that the minimization of the spectral radius assuming constant link weights is a convex optimization problem and the expressions derived subsume known protocols found in literature.
Journal ArticleDOI
H∞ performance for a class of uncertain stochastic nonlinear Markovian jump systems with time-varying delay via adaptive control method
TL;DR: In this article, the authors studied the H∞ performance for the uncertain recurrent neural networks with both nonlinear external disturbance and Markovian jump parameters, in which the time delay is varying.
Proceedings ArticleDOI
Adaptive control for jump parameter systems via nonlinear filtering
Peter E. Caines,Ji-Feng Zhang +1 more
TL;DR: In this article, an error analysis for the process of estimates generated by the Wonham filter when it is used for the estimation of the jump-Markov parameters of a linear stochastic system and further give bounds on certain functions of these estimates are presented.
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.