New criteria on finite-time stability of nonautonomous systems with delay and disturbance

This paper is concerned with the problem of finite-time stability for nonautonomous systems subject to time-varying delay and disturbance. Based on the piecewise estimate of the time-varying system matrices, we establish a new explicit criterion in terms of multiple linear matrix inequalities guaranteeing that the state trajectory does not exceed a certain threshold over a pre-specified finite-time interval. The main result of this paper generalizes and improves some existing results in the literature, and can also be extended to the more general nonlinear case. Finally, a numerical example is worked out to illustrate the effectiveness of the proposed method.