Title: Dissipativity analysis for nonlinear delayed differential systems with three kinds of time-varying delays

Authors: Yushan Chang; Xiaona Yang; Xian Zhang

Addresses: School of Mathematical Science, Heilongjiang University, Harbin, 150080, China; Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, China ' School of Mathematical Science, Heilongjiang University, Harbin, 150080, China; Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, China ' School of Mathematical Science, Heilongjiang University, Harbin, 150080, China; Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, China

Abstract: This work investigates the problems of global exponential stability analysis and dissipativity analysis for a class of nonlinear delayed differential systems concurrently affected by time-varying distributed, leakage and transmission delays. Sufficient conditions to guarantee that the considered nonlinear delayed differential systems are globally exponentially stable with dissipative level are presented by proposing a direct method based on system solutions. The conditions given in this paper consist of only several simple inequalities which are easily realised by applying the software tool YALMIP. The method proposed in this paper is quite simple and avoids the construction of Lyapunov-Krasovskii functionals, thus significantly reducing the computational effort. Finally, two simulation examples illustrate the applicability of the theoretical results.

Keywords: NDDSs; nonlinear delayed differential systems; dissipativity; global exponential stability; time-varying distributed delays; time-varying transmission delays; time-varying leakage delays.

DOI: 10.1504/IJAAC.2026.150561

International Journal of Automation and Control, 2026 Vol.20 No.1, pp.46 - 67

Received: 25 Feb 2024
Accepted: 20 May 2024
Published online: 17 Dec 2025 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article