Passive analysis and synthesis of uncertain Markovian jump systems in discrete-time

This paper provides the passive analysis and synthesis for Markovian jump systems in discrete-time with norm-bounded uncertainties. Based on the definition of passivity extended from deterministic systems, the sufficient condition on passivity of jump systems is given by stochastic Lyapunov functional. The passive controller via state-feedback is investigated to guarantee the stability and passivity of appropriate closed-loop system for all admissible uncertainties. It shows that a mode-dependent passive controller exists if a set of coupled linear matrix inequalities has solutions. The controller can be then constructed in terms of the solutions. Our results cover the results of passive analysis and synthesis for deterministic linear systems, with or without parametric uncertainties.