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
Finite-time H ∞ static output control of Markov jump systems with an auxiliary approach
TL;DR: This paper considers the finite-time H ∞ static output feedback control of Markov jump systems by introducing two new variables related to the original system state and output in terms of linear matrix inequalities (LMIs).
Journal ArticleDOI
Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters
Xu-Yang Lou,Baotong Cui +1 more
TL;DR: In this paper, the problem of stochastic stability for a class of time-delay Hopfield neural networks with Markovian jump parameters is investigated, where the jumping parameters are modeled as a continuous-time, discrete state Markov process.
Journal ArticleDOI
Finite Horizon $H_{2}/H_{\infty}$ Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise
Ting Hou,Weihai Zhang,Hongji Ma +2 more
TL;DR: A stochastic bounded real lemma (SBRL) is derived, which is used to establish a necessary and sufficient condition for the existence of the mixed finite horizon mixed H/sub 2/H/sub∞ control problem for discrete-time Stochastic linear systems subject to Markov jump parameters and multiplicative noise.
Journal ArticleDOI
Worst case control of uncertain jumping systems with multi-state and input delay information
TL;DR: Complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak-delay dependent stochastic stability with a prescribed H"~-performance.
Journal ArticleDOI
Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties
TL;DR: In this article, the authors considered the problem of stochastic stability and disturbance attenuation for a class of linear discretetime systems, and proposed a controller to guarantee the stability and robustness of the system.
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.