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Guaranteed cost PID control for uncertain discrete‐time stochastic systems with additive gain perturbations
Author(s) -
Mukaidani Hiroaki
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.259
Subject(s) - pid controller , control theory (sociology) , discrete time and continuous time , linear matrix inequality , controller (irrigation) , mathematics , stability (learning theory) , cost control , class (philosophy) , mathematical optimization , computer science , control (management) , engineering , control engineering , statistics , temperature control , agronomy , artificial intelligence , machine learning , biology
This paper investigates a novel design method for robust nonfragile proportional‐integral‐derivative (PID) control that is based on the guaranteed cost control (GCC) problem for a class of uncertain discrete‐time stochastic systems with additive gain perturbations. On the basis of linear matrix inequality (LMI), a class of fixed PID controller parameters is obtained, and some sufficient conditions for the existence of the GCC are derived. Although the additive gain perturbations are included in the feedback systems, both the stability of closed‐loop systems and adequate cost bound are attained. As a sequel, decentralized GCC PID for a class of discrete‐time uncertain large‐scale stochastic systems is also considered. Finally, the numerical results demonstrate the efficiency of the proposed controller synthesis.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society