- 學位論文
H∞ 連續模糊系統之控制設計-寬鬆穩定條件∞
SOS-based H∞ Fuzzy Controller Desging-Relaxation Method
摘要
李亞普諾夫能量函數V (x)對時間t微分會產生Q(x)微分項的 過程，為了要避免這個複雜的問題，則引入尤拉齊次多項式定理，本 論文主要在研究在連續模糊控制系統下的非二次穩定(Non-quadratic stability)，且加入H1性能指標的觀念，亦即非二次穩定李亞普諾 夫(Lyapunov function)能量函數V (x) = xT adj(Qz(x))x，而藉由尤拉 齊次多項式定理(Euler's Theorem for Homogeneous Functions)可導 出H1控制之李亞普諾夫不等式檢測穩定矩陣，輔以平方和(Sum of square)去檢驗其連續模糊系統之穩定條件，最後去模擬例子，來證明 此方法之正確性 i
並列摘要
Lyapunov energy function V (x) for time dierential will gener- ate Q(x) process derivative term, in order to avoid this complex is- sue, the lead to Euler's homogeneous polynomial theorem, this the- sis research in continuous fuzzy control system nonquadratic stable (Non-quadratic stability), and added performance concept of H1 , namely non-quadratic Lyapunov stability (Lyapunov function) energy function V (x) = xT adj(Qz(x))x , and by Euler homogeneous poly- nomial Theorem (Euler's Theorem for Homogeneous Functions) can be exported H1 control of Lyapunov inequality detection stabilizing matrix, supplemented square and (Sum of square) to test its stability conditions of continuous fuzzy systems, and nally to simulate exam- ple, to prove the correctness of this approach ii