Stability and stabilization of systems with a cyclical time-varying delay via delay-product-type looped-functionals

• Published in: Journal of the Franklin Institute Vol. 361; no. 7; p. 106775
• Main Authors: Liu, Yun-Fan, Wang, Hui-Ting, Fan, Yu-Long, Zhao, Wen-Xuan, Shangguan, Xing-Chen, Jin, Li
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.05.2024
• Subjects: Cyclical time-varying delay; Looped-functional; Stability analysis; State-feedback control; Cyclical time-varying delay; Stability analysis; Looped-functional; State-feedback control
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2024.106775

In this paper, the stability analysis and synthesis of systems with a cyclical time-varying delay are investigated. At first, the entire delay interval is divided into intervals of monotonically increasing and monotonically decreasing alternating cycles. Then, a Lyapunov-Krasovskii functional (LKF) with two delay-product-type looped-functionals is constructed based on different delay monotone intervals. For the generated quadratic function with respect to delay in the derivative of LKF, a matrix-injection-based method is utilized to obtain the negative-definite conditions of LKF’s derivative. A delay-dependent stability criterion with less conservatism is derived and the corresponding state-feedback control strategy is given consequently. Finally, a numerical example is utilized to show the superiority and the effectiveness of the proposed method, and a single-area power system under load frequency control is applied to verify the feasibility of the proposed control strategy.