H_\infty $H∞ control of linear singular time-delay systems subject to impulsive perturbations

• Published in: IET control theory & applications Vol. 11; no. 3; pp. 420 - 428
• Main Authors: Chen, Wu-Hua, Jiang, Renhong, Lu, Xiaomei, Zheng, Wei Xing
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 03.02.2017
• Subjects: Research Article; perturbation techniques; delay systems; LMI; linear systems; solvability; asymptotic stability; impulsive perturbations; impulse-free system; closed-loop system performance degradation; descriptor-type impulse-time-dependent Lyapunov functional; closed loop systems; L2-gain; H∞ control; state-feedback controller; linear singular time-delay systems; linear matrix inequalities; internally exponentially stable system; state feedback; sufficient condition; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2016.0166

This study addresses the problem of $H_\infty $H∞ control for linear singular time-delay systems subject to impulsive perturbations. Specifically, the impulses are allowed to be destabilising, i.e. they may degrade the closed-loop performance of the considered systems. With the aid of a descriptor-type impulse-time-dependent Lyapunov functional, a sufficient condition for the solvability of the problem is derived in terms of linear matrix inequalities (LMIs). By solving a set of LMIs, a desired state-feedback controller is found, which guarantees that the closed-loop system is impulse-free, internally exponentially stable, and achieves a prescribed $L_2$L2-gain. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed method.