New stability results for time-varying systems based an a modified detectability condition

The uniformly asymptotic stability is investigated from the output-to-state viewpoint for general nonlinear time-varying systems. Several criterions are proposed using some integral inequalities involving the output function and a new detectability condition. Furthermore, the existing results using the Lyapunov direct method, such as the Krasovskii-LaSalle invariance principle, a theorem of Aeyels and a theorem of Khalil for time-varying systems, are shown to be deduced for the proposed scheme. From these applications, it can be seen that, as the invariance principle of LaSalle is used in studying the stability of time-invariant systems, our results can be also used in studying the stability of time-varying systems