Finite-Time Stability for a Class of Underactuated Systems Subject to Time-Varying Disturbance

• Published in: Complexity (New York, N.Y.) Vol. 2020; no. 2020; pp. 1 - 7
• Main Authors: Li, Xiaodi, He, Xinyi, Yang, Dan, Wu, Jie
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 12.05.2020; Hindawi; John Wiley & Sons, Inc; Wiley
• Subjects: Asymptotic methods; Asymptotic properties; Control systems design; Dynamical systems; Inequality; Mathematical functions; Nonlinear systems; Stability
• ISSN: 1076-2787; 1099-0526
• DOI: 10.1155/2020/8704505

Based on the classical finite-time stability theory, the problem of finite-time stability (FTS) for time-varying nonlinear systems is investigated in this paper. Several FTS theorems involving global form and local form are presented, and an estimate of the settling-time of such systems is obtained. As an application, we consider the problem of asymptotic stabilization of the Brockett integrator subject to time-varying disturbance. By the switched finite-time controller design methodology, we establish a sufficient condition to guarantee the relative asymptotic stability. For Brockett-like integrator subject to time-varying disturbance, we achieve better convergence performance. Examples and their simulations are given to demonstrate the applicability of the proposed results.