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Improved fixed‐time stability results and application to synchronization of discontinuous neural networks with state‐dependent switching
Author(s) -
Abdurahman Abdujelil,
Jiang Haijun,
Hu Cheng
Publication year - 2021
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.5566
Subject(s) - differential inclusion , upper and lower bounds , synchronization (alternating current) , control theory (sociology) , mathematics , stability (learning theory) , controller (irrigation) , state (computer science) , type (biology) , settling time , artificial neural network , computer science , control (management) , topology (electrical circuits) , mathematical optimization , mathematical analysis , combinatorics , algorithm , engineering , artificial intelligence , ecology , control engineering , machine learning , step response , agronomy , biology
In this article, we considered the fixed‐time stability (FXT) of a type of discontinuous dynamical system. First, we introduced some new FXT stability results via variable substitutions and using inequality techniques, which are more accurately estimate the upper bound of settling time (ST). Then, based on the established results and using the differential inclusion theory, we investigated the FXT synchronization of a type of general neural networks (NNs) with state‐dependent switching coefficients and discontinuous neuron activation functions via introducing a type of discontinuous controller which is more simple compared to existing results. In addition, the estimated upper bound of ST shown to be independent to the initial values of considered drive‐response networks, and it is much smaller and nearer to the real synchronization time than those given in the previously published works. Lastly, two numerical examples are given to demonstrate the feasibility of our derived theoretical results. We believe that the results of this article can give some new insights for the FXT stabilization and FXT synchronization analysis of state‐dependent switching dynamics with or without discontinuous right‐hand sides.