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Robust Controller Design for Uncertain Linear Systems with Finite-frequency Specifications: A Polynomially Parameter-dependent Approach

Yingying Ren, Qing Li, Da-Wei Ding*, Wen Kang, and Yunxia Xia
International Journal of Control, Automation, and Systems, vol. 18, no. 11, pp.2808-2817, 2020

Abstract : This paper investigates the robust controller design for polytopic-type uncertain linear systems disturbed by external disturbances in restricted frequency ranges. The primary goal is to design a state-feedback controller, ensuring that the closed-loop system is robustly stable and keeps a prescribed finite-frequency (FF) disturbanceattenuation performance. For this purpose, a robust generalized Kalman-Yakubovich-Popov (KYP) lemma is applied to describe the finite-frequency specification, aiming at improving the disturbance-attenuation performance over the given frequency range. In this setting, more relaxed analysis conditions for robust stability and finitefrequency specifications are derived by introducing additional slack variables, which contain some existing conditions as special cases. Based on the homogeneous polynomially parameter-dependent (HPPD) technique, new controller design conditions in terms of linear matrix inequalities (LMIs) are developed. It is shown that the proposed finite-frequency design scheme can achieve a better disturbance- suppression performance in restricted frequency ranges than the existing ones, which is illustrated by an example about the satellite system.

Keyword : Finite-frequency specification, polytopic uncertainty, polynomially parameter-dependent Lyapunov functions, robust control.

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