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A Novel Approach to H2 and H∞ Filter Design for Discrete-time Switched Affine Systems
Zhenting Fu,Xiaozeng Xu,Xinyue Yang,Hongbin Zhang,Qunxian Zheng 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.6
This paper focuses on solving H2 and H∞ filtering problems for discrete-time switched affine systems. By constructing a discrete-time affine filtering error system, an observer-based filter and its corresponding switching function can be obtained by solving the linear matrix inequalities. For discrete-time switched affine systems, the performance indexes of the system in this neighborhood cannot be analyzed due to the existence of affine terms. The technique proposed in this note leads the system’s trajectory to the limit cycle so that the resulting conditions can consider the weighted H2 and H∞ performance level of the system. In addition, it is proved that the H2 and H∞ guaranteed cost is upper bounded and the upper boundaries are formulated by solving an optimization problem. Finally, two numerical examples are given to verify the theory.