Open AccessNew necessary and sufficient conditions for finite‐time stability of impulsive switched linear time‐varying systems
Author(s) -
Chen Guopei,
Yang Ying
Publication year - 2018
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.2017.0252
Subject(s) - dwell time , control theory (sociology) , lyapunov function , mathematics , piecewise , upper and lower bounds , stability (learning theory) , linear system , function (biology) , piecewise linear function , time derivative , lyapunov redesign , computer science , nonlinear system , control (management) , mathematical analysis , artificial intelligence , machine learning , medicine , clinical psychology , physics , quantum mechanics , evolutionary biology , biology
This note considers the problem of finite‐time stability (FTS) for impulsive switched linear time‐varying (LTV) systems. First, two improved necessary and sufficient conditions are proposed to verify the FTS of LTV by employing an indefinite Lyapunov function. Then, the results obtained are extended to study the FTS of impulsive switched LTV systems, two new necessary and sufficient conditions are given by using common indefinite Lyapunov function and piecewise indefinite Lyapunov functions. Compared with the existing results, the conditions obtained allow the time derivative of Lyapunov functions of subsystems to be indefinite and have a tighter upper bound, moreover, all subsystems are also allowed to be not FTS. Furthermore, the construction method of switching signal is given, moreover, using function‐dependent dwell time methods, three sufficient conditions of FTS are also proposed for the systems. Two numerical examples are given to illustrate the theoretical results.