Stability of stochastic systems with jumps
El-Kébir Boukas,Hailiang Yang +1 more
TLDR
In this article, it was shown that the guaranteed cost property of the proposed control strategy for the linear case can be proved for the nonlinear case as well as for the continuous case.Abstract:
This paper deals with stochastic stability of systems with Markovian jumps and Brownian motion. Mainly, we present sufficient conditions for quadratic stabilization of Ito type stochastic linear and nonlinear systems with Markovian jumps and Brownian motion using state feedback control. We also prove the guaranteed cost property of the proposed control strategy for the linear case.read more
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Stability of discrete-time linear systems with Markovian jumping parameters and constrained control
TL;DR: The approach of positively invariant sets is used to obtain new necessary and sufficient conditions for positive invariance, and enough conditions for stochastic stability for linear discrete-time systems with Markovian jumping parameters and constrained control.
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Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps
TL;DR: In this paper, a necessary and sufficient condition is established for mean-square quadratic stability and mean square quadratically stabilizability of continuous-time linear systems with Markovian jumps and norm-bound uncertainties in the parameters.
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H ∞ -control for linear time-delay systems with Markovian jumping parameters
TL;DR: In this paper, the robust H∞-control problem for uncertain continuous-time linear time-delay systems with Markovian jumping parameters is considered. But the uncertainties considered in this paper are of the norm-bounded type.
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Review of Some Control Theory Results on Uniform Stability of Impulsive Systems
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Observer design with guaranteed RMS gain for discrete-time LPV systems with Markovian jumps
TL;DR: In this paper, the authors consider the problem of designing state observers with guaranteed power-to-power (RMS) gain for a class of stochastic discrete-time linear systems that possess both measurable parameter variations and Markovian jumps in their dynamics.