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Robust decentralized H ∞ control for interconnected descriptor systems with norm‐bounded uncertainties
Author(s) -
Chen Ning,
Gui Weihua,
Zhai Guisheng
Publication year - 2009
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.83
Subject(s) - control theory (sociology) , decentralised system , mathematics , bounded function , norm (philosophy) , controller (irrigation) , nonlinear system , linear matrix inequality , robust control , mathematical optimization , control system , control (management) , computer science , engineering , law , artificial intelligence , mathematical analysis , agronomy , physics , electrical engineering , quantum mechanics , political science , biology
This paper considers a robust decentralized H ∞ control problem for interconnected descriptor systems. The uncertainties are assumed to be time‐invariant, norm‐bounded, and existing in both the system and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable H ∞ control with a specified disturbance attenuation level is derived in terms of a nonlinear matrix inequality (NMI). A two‐stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block‐diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is gradually modified from the nominal descriptor system (without uncertainties) to the original system with uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the usefulness of this method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society