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
On stability and stabilisation of continuoustime singular markovian switching systems
TL;DR: In this article, the class of continuous-time singular linear systems with Markovian switching with full and partial knowledge of the jump rates of the continuous time Markov process was considered and sufficient conditions for the system to be piecewise regular, impulse-free and stochastically stable were developed.
Journal ArticleDOI
Stability analysis of large-scale distributed networked control systems with random communication delays: A switched system approach
Kooktae Lee,Raktim Bhattacharya +1 more
TL;DR: A new reduced mode model for stability analysis of large-scale distributed networked control systems with random communication delays is proposed and a new method that estimates bounds for uncertain Markov transition probability matrix is provided to guarantee the system stability.
Journal ArticleDOI
Fault detection filter design for a class of nonlinear Markovian jumping systems with mode-dependent time-varying delays
TL;DR: The fault detection filter (FDF) design problem of a class of time-delayed and nonlinear Markovian jumping systems (MJSs) is considered and the Takagi–Sugeno fuzzy (TSF) modeling methods get sufficient conditions through which the stochastic stability of the TSF-M JSs can be guaranteed.
Journal ArticleDOI
Robust stabilization of stochastic Markovian jumping systems via proportional-integral control
Shuping He,Fei Liu +1 more
TL;DR: The proportional-integral control problems of stochastic Markovian jump systems with uncertain parameters are studied as a semidefinite programming one via disciplined convex optimization and a sufficient condition on the existence of PI controller is presented and proved by means of linear matrix inequality techniques.
Journal ArticleDOI
Brief paper: Stochastically exponential stability and stabilization of uncertain linear hyperbolic PDE systems with Markov jumping parameters
TL;DR: An SDLMI approach to the design of robust stabilizing controllers via state feedback is developed from the resulting stability condition, using the finite difference method and the standard linear matrix inequality (LMI) optimization techniques.
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.