Stability and Disturbance Attenuation for Markov Jump Linear Systems with Time-Varying Transition Probabilities

We address stability and disturbance attenuation for Markov jump linear systems where transition probabilities vary in a finite set. The time variation of the transition probabilities may be a priori known or unknown. Necessary and sufficient conditions for uniform stochastic stability and uniform stochastic disturbance attenuation are reported. In both cases, conditions are expressed as a set of finite-dimensional linear matrix inequalities that can be solved efficiently.