Bilinear Polynomial Fuzzy System Control

In this NSC proposal, we study a fuzzy bilinear feedback control problem for both continuous- and discrete-time polynomial fuzzy systems which are modeled as a Takagi-Sugeno fuzzy bilinear model. Based on homogeneous Lyapunov functions to guarantee energy decreasing for the bilinear systems, a set of stabilization conditions is obtained. The protruding feature for choosing homogeneous Lyapunov functions is the removal of dot P(x), for all xi in x for the continuous-time case. As to the discrete-time case, the structure of P(\tilde x) is formed by those states xi \in \tilde x whose Bi(x)=0 (i.e., states not being affected by it corresponding input due to Bi(x)=0).