Asymptotic stability analysis via indefinite Lyapunov functions and design of nonlinear impulsive control systems. (November 2020)

• Record Type: Journal Article
• Authors: Li, Huijuan; Liu, Anping
• Is Part Of: Nonlinear analysis. Volume 38(2020)
• Publication Date: 2020-11
• Subjects: Impulsive system -- Impulsive control -- Asymptotic stability -- Lyapunov function -- Indefinite Lyapunov function; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100936
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, we study asymptotic stability problem of nonlinear impulsive dynamic systems and design an impulsive controller for a chaotic system. We propose new sufficient conditions for asymptotic stability of the origin of nonlinear impulsive dynamic systems via indefinite Lyapunov functions. Indefinite Lyapunov functions may increase both during some continuous portion of the trajectory and at some impulses. We present two examples to demonstrate the effectiveness of our conclusions. Furthermore, based on the results, impulsive control is designed for a chaotic system. Highlights: Indefinite Lyapunov function for nonlinear impulsive dynamic systems is introduced. We propose new sufficient criteria for asymptotic stability via indefinite Lyapunov functions. Indefinite Lyapunov function may increase along some continuous portion and at some resetting times. Based on our results, impulsive control is designed for a chaotic system.