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Dwell‐time‐dependent conditions for exponential stability and hybrid L 2 × l 2 ‐gain of linear neutral time‐delay systems with impulsive effects
Author(s) -
Chen Jialin,
Chen WuHua,
Lu Xiaomei
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5502
Subject(s) - mathematics , control theory (sociology) , impulse (physics) , exponential stability , dwell time , timer , lyapunov function , piecewise , computer science , nonlinear system , mathematical analysis , medicine , clinical psychology , physics , control (management) , quantum mechanics , artificial intelligence , computer hardware , microcontroller
This article considers the problems of achieving exponential stability and finite hybrid L 2 × l 2 ‐gain with respect to continuous and discrete disturbances for linear neutral time‐delay systems with impulsive effects. In the framework of descriptor system representation, a piecewise timer‐dependent Lyapunov functional is introduced to analyze the double impacts of state‐delay and impulse‐dwell‐time on stability of the underlying system. This functional depends on the state over an impulse interval and the state over a delay interval. Its construction is based on a delay‐fractioning scheme which ensures all delay subintervals contains at most one impulse instant. The relations among the augmented state variables are explored by using the impulse‐timer functions and the Newton–Leibniz formula. It is proved that the positive definiteness property of the functional at nonimpulse instants is not necessary for ensuring stability. The hybrid L 2 × l 2 ‐gain analysis is carried out by jointly using the introduced functional and a discrete‐time Lyapunov function. The obtain criteria for exponential stability and hybrid L 2 × l 2 ‐gain are expressed in terms of linear matrix inequalities. Their effectiveness is verified through two numerical examples.