Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 67, Issue 10, Pages 5586-5593Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3123237
Keywords
Stability criteria; Asymptotic stability; Convergence; Time-varying systems; Nonlinear systems; Perturbation methods; Continuous time systems; Finite-time attractiveness; fixed-time attractiveness; nonlinear impulsive system
Funding
- National Natural Science Foundation of China [11771397]
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This article investigates the finite-time and fixed-time attractiveness problems for nonlinear impulsive systems by establishing general Lyapunov theorems and settling-time estimates. The results extend classical convergence theorems for nonlinear impulse-free systems and improve existing results for nonlinear impulsive systems.
In this article, the finite-time and fixed-time attractiveness problems are investigated for nonlinear impulsive systems. The aim of the proposed problems is to establish some general Lyapunov theorems and settling-time estimates for finite-time and fixed-time attractiveness of nonlinear impulsive systems by analysis technics. Moreover, some comparisons with the existing results are also given. The classical finite-time and fixed-time convergence theorems for nonlinear impulse-free systems are well extended to nonlinear impulsive systems by our results. Furthermore, the existing results of finite-time and fixed-time attractiveness for nonlinear impulsive systems are well improved. Finally, some simulations are utilized to illustrate the usefulness of the theoretical analysis.
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