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Stability analysis and systematic design of Takagi--Sugeno fuzzy control systems. (English) Zbl 1142.93373
Discussed are Takagi-Sugeno models of the form $$\gather R_i:\text{ If }x_1(t)\text{ is }F_{1i}\text{ and }x_2(t)\text{ is }F_{2i}\text{ and}\dots x_n(t)\text{ is }F_{ni}\text{ then }dx(t)/dt= A_ix(k)+ B_i u(t),\\ i= 1,2,\dots, 1,\endgather$$ where $x(t)= [x_1x_2 x_n]^T$ denotes a state vector and $(A_i, B_i)$ stands for the matrices of the corresponding local model. The extended Lyapunov stability criterion applied to the rule-based system presented above is concerned with the structural information about rules “activated” within some region and this helps relax the stability conditions (in which the $n\times n$ positive definite symmetric matrix $P$ involves only a subset of matrices $P_1,P_2,\dots, P_r$ pertaining to the individual rules). The mechanism of stability verification is then presented. Numeric examples are also included in this study.

MSC:
93C42Fuzzy control systems
93D05Lyapunov and other classical stabilities of control systems
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References:
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