Stability analysis and systematic design of Takagi--Sugeno fuzzy control systems
Discussed are Takagi-Sugeno models of the form \[ \begin{gathered} R_i:\text{ If }x_1(t)\text{ is }F_{1i}\text{ and }x_2(t)\text{ is }F_{2i}\text{ and}\dots x_n(t)\text{ is }F_{ni}\text{ then }dx(t)/dt= A_ix(k)+ B_i u(t),\\ i= 1,2,\dots, 1,\end{gathered} \] 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.
scientific article; zbMATH DE number 2153572