Global asymptotic stabilization via sampled-data control for a class of time-delayed systems

• Published in: Applied mathematics and computation 2025-04, Vol.490, p.129189, Article 129189
• Main Authors: Wang, Xin, Ding, Shihong, Ma, Li, Mei, Keqi
• Format: Article
• Language: English
• Subjects: Adding a power integrator; Global asymptotic stabilization; Homogeneous domination method; Lyapunov-Krasovskii functionals; Sampled-data controller
• ISSN: 0096-3003
• DOI: 10.1016/j.amc.2024.129189

This article addresses the issue of global asymptotic stabilization (GAS) for a group of linearly uncontrollable and unobservable time-delayed systems with uncertain control gains. As a result of the use of a nonsingular transformation and time rescaling, the group of nonlinear integrators with large delays are transformed into nonlinear integrators with small delays. Then, after applying both the homogeneous domination method and Lyapunov-Krasovskii (L-K) functionals, and revamping the adding a power integrator, we construct L-K functionals and a homogeneous non-smooth sampled-data controller, achieving GAS of the considered uncontrollable and unobservable time-delayed systems. Finally, an example is given to verify the efficiency of the proposed method. •By revamping the adding a power integrator, homogeneous domination approach and constructing the L-K functionals, a non-smooth sampled-data control scheme is explicitly presented. Consequently, the linearly uncontrollable and unobservable time-delayed system is globally asymptotically stable.•Different from [31,32], where the power constants pi≥1 in linearly uncontrollable and unobservable systems are odd positive integers or require p1≥p2≥…≥pn−1≥pn=1, the constraints on the power constants given in this article are relaxed and pi≥1, i=1,2,…,n belong to positive integers.•The time-delayed systems with strong nonlinearity, which cannot be handled by linear or smooth nonlinear feedback, have been examined. A sampled-data control scheme is considered in this paper and the non-smooth sampled-data controller is designed successfully for time-delayed systems with strong nonlinearity.