New stability analysis of T-S fuzzy system with robust approach
The paper is concerned with the continuous Takagi-Sugeno rule-based model whose rules \((R_i)\) assume the form \[ R_i:\text{if }z_1 \text{ is }F_i(1) \text{ and }z_2\text{ is }F_i(2) \text{ and}\dots \text{and } z_n\text{ is }F_i(n)\text{ then }dx/dt=A_i {\mathbf x}(t), i=1,2,\dots,r \] with \({\mathbf x}\) being a state vector, \({\mathbf z}=[z_1 z_2 \dots z_n]\) denoting a vector of control variables, and \(F_j(i)\) forming fuzzy sets occurring in the \(i\)-th rule. Rewriting this model as \[ dx/dt=A_0 x(t)+\sum^n_{i=1} \mu_iA_i {\mathbf x}(t), \quad A_0={1\over r}\sum^r_{i=1} A_i \] where \(\Delta A_i=A_i-A_0\) and \(\mu_i\) is a degree of activation (firing) of the \(i\)-th rule, sufficient conditions of asymptotic stability of this model are formulated. A simple numerical example illustrates the proposed method.
scientific article; zbMATH DE number 1794862