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

In this paper, the problem of H∞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∞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.