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
Output Feedback Stabilization and Disturbance Attenuation of Time-Delay Systems with Markovian Jump Parameters
TL;DR: In this paper, the authors investigated the problems of stochastic stabilization and control for a class of linear time-delay systems with Markovian jump parameters via output feedback, where the jumping parameters were modelled as continuous-time, discrete-state Markov process.
Proceedings ArticleDOI
Optimal filtering and control of linear systems with Markov perturbations
TL;DR: In this paper, the authors studied the optimal filtering and control problem for non-gaussian initial conditions for noisy observations of the state X and perfect observations of Z under technical assumptions.
Journal ArticleDOI
Stabilization and Optimization of Discrete-Time Markovian Jump Linear Systems via Mode Feedback Control
TL;DR: In this article , a mode feedback control mechanism is adopted to adjust the mode transition probability matrix, which is referred to as the switching law design, and the optimal mode feedback controller is sought to minimize a quadratic performance index containing both the system state and the feedback control input.
Journal ArticleDOI
On stochastic stabilization via non-smooth control Lyapunov functions
TL;DR: In this paper , it is shown that if there is a, generally non-smooth, control Lyapunov function, the given stochastic dynamical system can be practically stabilized in the sample-and-hold mode, meaning that the control actions are held constant within sampling time steps.
Journal ArticleDOI
Moment exponential stability analysis of Markovian jump stochastic differential equations with uncertain transition jump rates
TL;DR: Sufficient conditions for testing the stability of Markovian jump stochastic differential equations are established, and some numerical examples to illustrate the effectiveness of the results 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.