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

[摘要] This paper is concerned with the problem of $$H_{\infty }$$ H ∞ 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 $$H_{\infty }$$ H ∞ performance index. By using the Lyapunov functional approach and introducing some zero equations, a new condition for $$H_{\infty }$$ H ∞ 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.

[学科分类] 自动化工程

[关键词] 2-D systems;Markovian jump;Model reduction;\(H_{\infty }\) performance;Linear matrix inequalities