Finite-Time and Fixed-Time Attractiveness for Nonlinear Impulsive Systems

Hongxiao Hu, Bei Gao, Liguang Xu

2021IEEE Transactions on Automatic Control42 citationsDOI

Abstract

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.

Topics & Concepts

Nonlinear systemSettling timeImpulse (physics)Control theory (sociology)Convergence (economics)AttractivenessMathematicsApplied mathematicsComputer scienceMathematical optimizationControl (management)EngineeringControl engineeringPhysicsArtificial intelligenceStep responseQuantum mechanicsPsychologyEconomicsPsychoanalysisEconomic growthNeural Networks Stability and SynchronizationStability and Controllability of Differential EquationsMathematical and Theoretical Epidemiology and Ecology Models