Dwell‐time‐dependent conditions for exponential stability and hybrid L2 × l2‐gain of linear neutral time‐delay systems with impulsive effects.

This article considers the problems of achieving exponential stability and finite hybrid L2 × l2‐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 L2 × l2‐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 L2 × l2‐gain are expressed in terms of linear matrix inequalities. Their effectiveness is verified through two numerical examples. [ABSTRACT FROM AUTHOR]