Model reduction of A class of Markov jump nonlinear systems with time-varying delays via projection approach

In this paper, the problem of H_∞ model reduction for a class of discrete-time Markov jump nonlinear systems with time-varying delays is investigated. Based on the Lyapunov-Krasovskii functional method, sufficient stability conditions in terms of strict LMIs are derived for the model error system. Projection approach is employed to construct a reduced-order model such that the model error system is asymptotically stable and preserves a guaranteed H_∞ performance. A numerical example is presented to illustrate the effectiveness of the developed theoretical results and to make comparisons among systems with different structures and parameters.