Open AccessDwell‐time‐dependent stability results for impulsive systems
Author(s) -
Shao Hanyong,
Zhao Jianrong
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.1350
Subject(s) - aperiodic graph , dwell time , mathematics , control theory (sociology) , stability (learning theory) , lyapunov function , computer science , nonlinear system , physics , medicine , clinical psychology , control (management) , artificial intelligence , machine learning , combinatorics , quantum mechanics
This study is concerned with the dwell‐time stability for impulsive systems under periodic or aperiodic impulses. A Lyapunov‐like functional approach is established to study the stability for impulsive systems. The Lyapunov‐like functional is time‐varying and decreasing but is not imposed definite positive nor continuous. A specific Lyapunov‐like functional is constructed by introducing the integral of state together with the cross‐terms of the integral and impulsive states. A tight bounding is obtained for the derivative of this functional with the help of the improved Jensen inequality reported recently and the integral equation of the impulsive system. On the basis of the Lyapunov‐like functional approach, new dwell‐time‐dependent stability results with ranged dwell‐time, maximal dwell‐time and minimal dwell‐time are derived for periodic or aperiodic impulsive systems. The stability results have less conservatism than some existing ones, which are illustrated by numerical examples.