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Stabilization of discrete‐time singular Markovian jump repeated vector nonlinear systems
Author(s) -
Wang Guoliang,
Zhang Qingling,
Yang Chunyu
Publication year - 2015
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.3383
Subject(s) - uniqueness , control theory (sociology) , nonlinear system , mathematics , stability (learning theory) , linear matrix inequality , discrete time and continuous time , controller (irrigation) , jump , series (stratigraphy) , mode (computer interface) , computer science , control (management) , mathematical optimization , mathematical analysis , paleontology , statistics , physics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology , operating system
Summary This paper studies the control problem for discrete‐time singular Markovian jump systems with repeated vector nonlinearities. Sufficient conditions for stochastic stability are established, where the uniqueness of solution to the underlying system is also guaranteed. Then, a series of formulations of stabilizing conditions is further developed to design mode‐dependent and mode‐independent controllers by using the linear matrix inequality approach. Based on the proposed results, more special cases for stabilizing controller are considered. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.