Finite-time stabilization for a class of switched time-delay systems under asynchronous switching

• Published in: Applied mathematics and computation Vol. 219; no. 11; pp. 5757 - 5771
• Main Authors: Zong, Guangdeng, Wang, Ruihua, Zheng, Wei Xing, Hou, Linlin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2013
• Subjects: Asynchronous switching; Average dwell time; Control systems; Disturbances; Electronics; Finite-time stability; Finite-time stabilization; Mathematical models; Nonlinearity; Stabilization; State feedback; Switched time-delay systems; Switching; Switched time-delay systems; Finite-time stability; Average dwell time; Finite-time stabilization; Asynchronous switching
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2012.11.078

Switched control systems can be used to describe many practical processes with switching phenomena, such as power electronics, mechanical systems, etc. In this paper, the problem of finite-time stabilization under asynchronous switching is dealt with for a class of switched time-delay systems with nonlinear disturbances. Firstly, the nonlinear uncertainties are transformed into the linear time-varying forms via the differential mean value theorem under some assumptions. Secondly, by applying the average dwell time method and convexity principle, a finite-time stability condition for the unforced switched time-delay system is established. Finally, an asynchronous switching state feedback controller is designed which renders the considered system finite-time stable. A numerical example is provided to show the effectiveness of the developed results.