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: asymptotic stability; closed loop systems; closed‐loop system performance degradation; delay systems; descriptor‐type impulse‐time‐dependent Lyapunov functional; H∞ control; impulse‐free system; impulsive perturbations; internally exponentially stable system; L2 ‐gain; linear matrix inequalities; linear singular time‐delay systems; linear systems; LMI; Lyapunov methods; perturbation techniques; solvability; state feedback; state‐feedback controller; sufficient condition
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2016.0166

This study addresses the problem of 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 L2 ‐gain. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed method.