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
More filters
Journal ArticleDOI
Exponential stability in mean square for a general class of discrete-time linear stochastic systems
Vasile Dragan,Toader Morozan +1 more
TL;DR: In this article, three different definitions of the concept of mean square exponential stability in mean square are introduced and it is shown that they are not always equivalent and that they may not always be equivalent.
Journal ArticleDOI
Robustness of Stochastic Discrete-Time Switched Linear Systems With Application to Control With Shared Resources
TL;DR: It is shown that a wide class of shared resources control strategies can be modeled by a stochastic jump linear system involving two stochastics processes, including Markov chains and independent and identically distributed switching processes.
Journal ArticleDOI
Almost Sure Stability and Stabilization of Markovian Jump Systems With Stochastic Switching
TL;DR: In this paper , the exponential almost sure (EAS) stability and stabilization problems of continuous-time Markovian jump systems with additional stochastic switches are addressed by applying a method to its stochastically transfer matrix.
Journal ArticleDOI
Stability analysis of power system with multiple operating conditions considering the stochastic characteristic of wind speed
TL;DR: In this article, a new method to analyze the stability of power system with multiple operating conditions considering the stochastic characteristic of wind speed is proposed, which is based on the Weibull model.
Journal ArticleDOI
Quantum Lyapunov exponents beyond continuous measurements
TL;DR: This work proposes an alternative generalization based on the unraveling of quantum master equation into an ensemble of "quantum trajectories," by using the so-called Monte Carlo wave-function method and demonstrates that the transition to quantum chaos matches the period-doubling route to chaos in the corresponding mean-field system.
References
More filters
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.