Monotone-delay-interval-based Lyapunov functionals for stability analysis of systems with a periodically varying delay

• DOI: 10.1016/j.automatica.2021.110030
• Publication Date: 2021-11-24T20:59:59Z
• Authors: Hong-Bing Zeng; Yong He; Kok Lay Teo
• Keywords: 0209 industrial biotechnology; 0202 electrical engineering, electronic engineering, information engineering; 02 engineering and technology

Abstract This paper focuses on the stability analysis of linear time-invariant (LTI) systems with a time-varying delay. The delay is assumed to be periodically varying. Furthermore, for each period, the delay is divided to be on one monotone increasing interval and one monotone decreasing interval. By capturing the monotone characteristic of the delay intervals, two looped functions are proposed for the monotone increasing intervals and the monotone decreasing intervals, respectively. A novel monotone-delay-interval-based Lyapunov functional is established based on these looped functions. On this basis, less conservative stability conditions are obtained. Finally, a benchmark example is provided to demonstrate the efficiency and the benefits of the proposed approach.