$$H_{\infty }$$ Model Reduction for 2-D Discrete Markovian Jump Systems

Abstract

This paper is concerned with the problem of $$H_{\infty }$$ model reduction for two-dimensional (2-D) discrete Markovian jump systems. The mathematical model of 2-D Markovian jump systems is described by the Fornasini–Marchesini (F–M) second model. Our attention is focused on the design of a 2-D reduced-order model, which ensures the model error system to be stochastically stable and has a prescribed $$H_{\infty }$$ performance index. By using the Lyapunov functional approach and introducing some zero equations, a new condition for $$H_{\infty }$$ performance analysis of model error system is developed. Based on this condition, the desired reduced-order model parameters can be obtained by solving a set of linear matrix inequalities. Two examples are presented to show the effectiveness of the proposed method.