在這個研究計畫中，我們藉由一個齊次多項式(Homogeneous Lyapunov)函數提出一個雙線性迴授控制問題。所提出的研究計畫可證明現存單一的 (Single quadratic Lyapunov) 函數的二次穩定(quadratic)的方法是多項式Lyapunov理論中的特例。利用齊次多項式函數(Homogeneous Lyapunov)，研究方法是基於SOS求雙線性系統的迴授控制，這研究計劃將實現以一步驟的迴授控制使多項式模糊雙線性控制系統達到穩定。目前發表的多項式理論都是以單線性輸入的模糊控制系統。對於下示之多項式雙線性系統\dot x = A(x) + B(x)u + N(x)xu 存在 xu 相乘的雙線性結構。經過多方研究與搜尋，從未有雙線性的多項式模糊控制系統的相關研究，因此申請者認為有新的領域可將目前多項式的成果應用於雙線性多項式模糊系統，將現存的SOS充分條件，繼續推廣至多項式雙線性模糊系統的穩定性研究，甚至以後可再推廣至觀測器的研究。 ;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).
