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
Stability and output feedback stabilization for systems with Markovian switching and impulse effects
Shen Cong,Yun Zou,Yijun Zhang +2 more
TL;DR: In this article, the authors investigate the exponential stability in the mean square sense for the systems with Markovian switching and impulse effects, and establish a stability criterion based on the statistic property of the Markov process, which makes the closed-loop system exponentially stable.
Journal ArticleDOI
Asymptotic stability of a class of nonlinear stochastic systems undergoing Markovian jumps
Rh H. Huan,W. Q. Zhu,Zg G. Ying +2 more
TL;DR: In this paper, an approximate method is presented to assess the asymptotic stability, with probability one, of nonlinear, multi-degree-of-freedom, Markovian-jump quasi-nonintegrable Hamiltonian systems subjected to stochastic excitations.
Proceedings ArticleDOI
Occupant-location-catered control of IOT-enabled building HVAC systems
TL;DR: A structured Markov Jump-Linear System model is developed which captures the diffusive heat-exchange process in the building, stochastic occupant movement, and feedback control enacted by the HVAC system.
Journal ArticleDOI
Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump
TL;DR: In this paper, the semi-infinite time optimal control for a class of stochastically excited Markovian jump nonlinear systems is investigated using stochastic averaging, each form of the system is reduced to a one-dimensional partially averaged Ito equation of total energy.
Proceedings ArticleDOI
/spl Hscr//sub /spl infin// filtering for Markovian jump linear systems
C.E. de Souza,Marcelo D. Fragoso +1 more
TL;DR: In this article, a methodology for designing Markovian jump linear filters which ensure a prescribed bound on the /spl Lscr/sub 2/-induced gain from the noise signals to the estimation error was proposed.
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.