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CONTROL LAW FOR QUADRATIC STABILIZATION OF PERTURBED FUZZY TIME‐DELAY LARGE‐SCALE SYSTEMS VIA LMI
Author(s) -
Wang RongJyue
Publication year - 2006
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 - 10.1111/j.1934-6093.2006.tb00287.x
Subject(s) - control theory (sociology) , mathematics , schur complement , complement (music) , fuzzy logic , fuzzy control system , quadratic equation , state (computer science) , controller (irrigation) , control (management) , computer science , algorithm , biochemistry , eigenvalues and eigenvectors , physics , geometry , quantum mechanics , artificial intelligence , complementation , biology , agronomy , gene , phenotype , chemistry
In this paper, the perturbed continuous‐time large‐scale system with time delays is represented by an equivalent Takagi‐Sugeno type fuzzy model. First, two types of decentralized state feedback controllers are considered in this paper. Based on the Riccati‐type inequality, the Razumikhin theorem, and the delay‐dependent Lyapunov functional approach, some controller design approaches are proposed to stabilize the whole fuzzy time‐delay system asymptotically. In these design methods, both the delay‐independent and delay‐dependent stabilization criteria are derived. By Schur complement, these sufficient conditions can be easily transformed into the problem of LMI's. Moreover, the systems with all the time‐delays τ l ij ( t ) are the same for all rules ( i.e. , τ l ij ( t ) = τ m ij ( t ) = τ ij for all l =m ); the authors also propose a simpler and less conservative stabilizing criteria. A numerical example is given to illustrate the control design and its effectiveness.