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Krasovskii and Razumikhin criteria on input‐to‐state stability of discrete‐time time‐varying switched delayed systems
Author(s) -
Peng Shiguo,
Deng Feiqi,
Xiao Mingqing,
Wang Yonghua
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4935
Subject(s) - dwell time , discrete time and continuous time , control theory (sociology) , mode (computer interface) , stability (learning theory) , state (computer science) , function (biology) , mathematics , computer science , algorithm , control (management) , artificial intelligence , statistics , medicine , clinical psychology , machine learning , evolutionary biology , biology , operating system
Summary 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.