根據線性參數變化(LPV) 系統的強健性穩定之最新的理論, 本計畫使用波雅定理(P´olya Theorem) 之代數性質(algebraic property) 來建立以共同李亞普諾夫函數為基礎之寬鬆參數相依線性矩陣不等式(PD-LMI) 組, 因為這些參數相依線性矩陣不等式皆為從屬函數¹的齊次多項式, 故必須轉成依據由各頂點所激發之線性矩陣不等式組來檢驗系統穩定之充分條件; 進而探討二次李亞普諾夫函數二次穩定的必要條件(necessity) 之存在性問題。最後, 藉由文獻上的例子說明提出方法的可行性及實用性。 ; Deducing from robust stability of linear parameter varying (LPV) systems, we investigate the necessary and sufficient stability/stabilization conditions characterized by parameter-dependent LMI formulations in terms of firing strength belonging to the unit simplex, exploiting the algebraic property of P´olya’s Theorem to construct a family of finite-dimensional LMI relaxations whose matrix solutions progressivley converge towards a common Lyapunov P mmatrix, leading to the necessary condition for the existence of quadratic function Lyapunov assuring quadratic stability. Finally the utility of the proposed method is illuminated by an example. ; 研究期間 9708 ~ 9807
