Robust H∞ control of markovian jump linear systems with uncertain switching probabilities

Abstract

This paper is concerned with the robust H∞ control of Markovian jump linear systems with uncertain switching probabilities. The uncertain system under consideration involves norm-bounded uncertainties in system matrices and element-wise bounded uncertainties in the mode transition rate matrix. A new criterion is established to test the robust H ∞ performance in terms of linear matrix inequalities and a su±cient condition is addressed for constructing a robust state-feedback controller such that the closed-loop system is robustly mean square stable and has the desired H∞ performance level. A globally convergent algorithm involving convex optimization is also proposed to find such controllers effectively. Finally, a numerical example illustrates the usefulness of the developed theory. Copyright © 2005 IFAC.