Electrical Engineering and Systems Science > Systems and Control
[Submitted on 2 Sep 2025
]
Title: Finite-Time Stabilization of a Class of Nonlinear Systems in Hilbert Space
Title: 有限时间区间内希尔伯特空间中一类非线性系统的稳定化
Abstract: This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the convergence objective (finite-time) and the rejection of perturbations are achieved. Second, we consider a class of nonlinear systems and design a feedback control that ensures the closed-loop system is finite-time stable. All proofs presented in this paper regarding convergence are based on Lyapunov theory. The existence of solutions to the closed-loop system and its well-posedness are established using maximal monotone theory. To illustrate the applicability of the theoretical results, a heat equation is considered as an application of the main results.
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