Local input-to-state stabilization of time-delay systems subject to actuator saturation and external disturbance

• Published in: Journal of the Franklin Institute Vol. 357; no. 7; pp. 4154 - 4170
• Main Authors: Ding, Yucai, Cheng, Jun, Liu, Hui, Zhong, Shouming
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.05.2020; Elsevier Science Ltd
• Subjects: Actuators; Domains; Effectiveness; Linear matrix inequalities; Mathematical analysis; Matrix; Numerical analysis; Saturation; Stabilization; Time delay systems
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2020.01.020

In this paper, we deal with the problem of local input-to-state stabilization for a class of time-delay systems subject to actuator saturation and external disturbance. The saturation function is described by a polytopic representation. Based on the Lyapunov–Krasovskii functional method, sufficient conditions on local input-to-state stabilization are derived in terms of linear matrix inequalities (LMIs). Meanwhile, the maximal domain of the initial states is estimated such that the state trajectories starting from this domain are bounded. In the absence of the external disturbance, the exponential stabilization problem is also considered. Three numerical examples are provided to illustrate the feasibility and effectiveness of the derived results.