Dissipativity-based model reduction for discrete-time piecewise homogeneous Markov jump Lur´e systems

This paper addresses the dissipativity-based model reduction problem for a class of Markov jump Lur´e systems with time varying transition probabilities in discrete-time domain. The time-varying character of transition probabilities is considered to be finite piecewise homogeneous. A reduced-order model is constructed to approximate the discrete-time Markov jump Lur´e systems, such that the error systems are stochastically stable and strictly (Q, S, R)-γ-dissipative. Sufficient conditions for the existence of desired reduced-order models are derived in terms of linear matrix inequalities. A numerical example is presented to show the effectiveness of the proposed theories.