Brief On robust stabilization of Markovian jump systems with uncertain switching probabilities

Authors:
Junlin Xiong;James Lam;Huijun Gao;Daniel W. C. Ho
Affiliations:
Department of Mechanical Engineering, University of Hong Kong, Hong Kong;Department of Mechanical Engineering, University of Hong Kong, Hong Kong;Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China;Department of Mathematics, City University of Hong Kong, Hong Kong
Venue:
Automatica (Journal of IFAC)
Year:
2005

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Abstract

This brief paper is concerned with the robust stabilization problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertain Markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix. First, a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities. Then, a sufficient condition is proposed for the design of robust state-feedback controllers. A globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively. Finally, a numerical simulation is used to illustrate the developed theory.