Exponentially weighted integral input-to-state stability of nonlinear control systems with time delay

Stability analysis of nonlinear system is an important problem in control and engineering field. Input-to-state stability is one of the important concepts which have been introduced into nonlinear control systems. This paper generalizes the input-to-state stability to exponentially weighted integral input-to-state globally uniformly stable and exponentially weighted integral input-to-state globally uniformly asymptotically stable of nonlinear control systems with time delay. By developing the method of Lypaunov-Razumikhin technique, several results of exponentially weighted integral input-to-state stability are derived. Relevant examples are provided to illustrate the correctness of the obtained results.