Robust H-infinity Control of Markovian Jump linear Systems with Uncertain Switching Probabilities

This paper is concerned with the robust H-infinity control of Markovian jumplinear systems with uncertain switching probabilities. The uncertain systemunder consideration involves norm-bounded uncertainties in system matrices andelement-wise bounded uncertainties in the mode transition rate matrix. A newcriterion is established to test the robust H-infinity performance in terms oflinear matrix inequalities and a sufficient condition is addressed forconstructing a robust state-feedback controller such that the closed-loopsystem is robustly mean square stable and has the desired H-infinityperformance level. A globally convergent algorithm involving convexoptimization is also proposed to find such controllers effectively. Finally, anumerical example illustrates the usefulness of the developed theory.