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A new approach for stabilizing nonlinear systems with time delays
Author(s) -
Er M. J.,
Lin D. H.
Publication year - 2002
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.10022
Subject(s) - continuous stirred tank reactor , control theory (sociology) , compensation (psychology) , nonlinear system , stability (learning theory) , lyapunov stability , computer science , salient , lyapunov function , stability criterion , linear matrix inequality , mathematics , exponential stability , mathematical optimization , engineering , control (management) , discrete time and continuous time , artificial intelligence , physics , quantum mechanics , psychology , statistics , chemical engineering , machine learning , psychoanalysis
Abstract The proportional parallel distributed compensation (PPDC) approach is utilized to stabilizetime‐delay systems modeled by Takagi‐Sugeno fuzzy models in this article. Based on the Lyapunovstability analysis, stability conditions concerning asymptotical stability of time‐delay systems areestablished. The main advantage of the PPDC approach over the parallel distributed compensation (PDC)approach is that fewer adjustable parameters are needed to ensure stability. Moreover, the procedure of findingcommon matrices P and S is simplified and the number of Lyapunov inequalities is reduced significantly. Theentire PPDC design procedure employing linear matrix inequalities (LMIs) is presented. A numericalexample of stabilizing a continuous stirred tank reactor (CSTR) is given to illustrate salient featuresof the new approach. © 2002 Wiley Periodicals, Inc.