Robust finite‐frequency filter design for linear uncertain systems using polynomially parameter‐dependent approach

Abstract

This study investigates the problem of robust filter design for continuous-time linear uncertain systems affected by external noises in finite-frequency (FF) ranges. The objective is to design an admissible filter guaranteeing asymptotic stability of the filtering error system with a prescribed FF noise attenuation level. To this end, homogenous polynomially parameter-dependent Lyapunov functions are used to assess the stability of the filtering error system, and robust FF bounded realness lemma is used to describe the noise attenuation specifications. Polynomially parameter-dependent matrices and some scalars are introduced to facilitate filter design and reduce conservatism. Moreover, a sequential convex approximation method is used to replace the non-convex constrained set with a convex feasible one. On this basis, an iterative algorithm is developed to calculate the filter parameters. It is demonstrated that the proposed robust FF filter can achieve a better noise attenuation performance in the FF range than the existing ones in the literature. An example about F-18 aircraft model is given to illustrate the effectiveness of the proposed method.