Control of discrete fuzzy systems: Uncertainty and guaranteed performance (Q1384043)

The authors introduce a design scheme for switching-type robust control in discrete Takagi-Sugeno fuzzy models. The standard model being commonly encountered in the literature comes in the form of a rule-based structure where the \(i\)th many-input single-output rule reads as: -- if \({\mathbf x}_1(k)\) is \(A_1\) and \({\mathbf x}_2(k)\) is \(A_2\) and \dots and \({\mathbf x}_n(k)\) is \(A_n\) and \({\mathbf u}_1(k)\) is \(B_1\) and \({\mathbf u}_2(k)\) is \(B_2\) and \dots and \({\mathbf u}_m(k)\) is \(B_m\) then \({\mathbf x}_i(k+1)=A_i{\mathbf x}(k)+B_i{\mathbf u}(k)\), where \({\mathbf x}_i\in\mathbb{R}^n\) and \({\mathbf u}_i\in\mathbb{R}^n\). This model is augmented by time-varying and bounded uncertainties \({\mathbf q}(k)\) standing in the parameters of the model, namely \(A_i({\mathbf q}(k))\) and \(B_i({\mathbf q}(k))\) where \({\mathbf q}(k)\in\Omega\) and \(\Omega\) is given and compact. The robust control scheme is given. Its stability is discussed. Illustrative examples are also shown.