Brief paper: New results on stabilization of Markovian jump systems with time delay

Authors:
Zhongyang Fei;Huijun Gao;Peng Shi
Affiliations:
Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, 150001, PR China;Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, 150001, PR China;Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd, CF37 1DL, UK and School of Engineering and Science, Victoria University, Melbourne, Vic 8001, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

This paper studies the problem of stochastic stabilization for a class of Markovian jump systems with time delay. A new delay-dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel Lyapunov-Krasovskii functional (LKF) approach. The equivalence and superiority to existing results are demonstrated. Then a state feedback controller, which guarantees the stochastic stability of the closed-loop system, is designed. Illustrative examples are provided to show the reduced conservatism and effectiveness of the proposed techniques.