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

Journal of control, automation and electrical systems

article

Badie, Khalid¹  Alfidi, Mohammed¹  Chalh, Zakaria¹ 

[1] Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University

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

DOI  :  10.1007/s40313-020-00662-0

学科分类：自动化工程

来源: Springer

【 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.

【 授权许可】

CC BY