Krasovskii and Razumikhin criteria on input-to-state stability of discrete-time time-varying switched delayed systems

In this article, we are concerned with the problem on input-to-state stability (ISS) for discrete-time time-varying switched delayed systems. Some Krasovskii and Razumikhin ISS criteria are provided by using the notions of uniformly asymptotically stable (UAS) function and mode-dependent average dwell time (MDADT). With the help of the concept of UAS function, the advantage of our results in this article is that the coefficients of the first-order difference inequalities for the mode-dependent Krasovskii functionals and mode-dependent Razumikhin functions are allowed to be time-varying, mode-dependent, and can even take both positive and negative values, and the whole switched system can be allowed to have both ISS subsystems and non-ISS subsystems. With the aid of the notion of MDADT, each subsystem can have its own average dwell time. As an application, we also provide an ISS criterion for discrete-time time-varying switched delayed Hopfield neural networks with disturbance inputs. Numerical simulations verify the effectiveness of the established criteria.