Practical Input-to-State Stability of Nonlinear Systems with Time Delay

An investigation of the input-to-state practical stability (ISpS) and the integral input-to-state practical stability (iISpS) of nonlinear systems with time delays (NSWTDs) is presented in this paper. The ISpS and iISpS of the systems are obtained by using a continuously differentiable Lyapunov–Krasovskii functional (LKF) within-definite derivative, which generalizes the classical LKF with a positive definite derivative. As a result, the uniform practical asymptotic stability (UPAS) criteria of NSWTD were also given by using the proposed LKF.