Indefinite Krasovskii and Razumikhin Stability for Nonlinear Positive Time-Varying Systems

This paper addresses the stability of nonlinear positive time-varying systems (TVSs) with time delays in terms of Krasovskii functional and Razumikhin function, respectively. The presented functional and function allow the time derivatives to be nondecreasing. First, an indefinite Krasovskii functional is constructed for the systems and some linear time-varying conditions are addressed for the stability. The indefinite Krasovskii functional is also used for linear positive TVSs. Then, an indefinite Razumikhin function is constructed for the stability of nonlinear positive TVSs. It is shown that the indefinite Krasovskii functional and Razumikhin function are less conservative than existing definite functionals and functions. The effectiveness of the theoretical findings is verified via one example.