本論文主要研究連續模糊系統之非二次穩定(non-quadratic stability)
條件下的片段式李亞普諾夫函數，再加入切換式觀測器去提升
追蹤狀態的效能。藉由改變穩定度條件裡的變數，使數個李亞普諾
夫函數得以交錯，重新組成一片段式李亞普諾夫函數，其中皆以尤拉
齊次多項式定理建立非二次李亞普諾夫函數(non-quadratic Lyapunov
function)，其形式為
V (x) = xTP(x)x = 1
g(g􀀀1)xT∇xxV (x)x。
然後再使用求得的李亞普諾夫函數之交錯時間點去設計切換式觀
測器，在設計切換式觀測器的過程中，也去探討不同類型的系統(系
統矩陣是否包含待估測狀態)，所需的觀測器格式與穩定度條件。
例題模擬部分，先以泰勒級數建模得出模糊系統，且以非二次的
李亞普諾夫函數及對時間的變化率作為穩定的條件，加入片段式結構
後，再以平方和方法(Sum-of-Squares) 來檢驗模糊系統的穩定條件，
並設計出合適的切換式觀測器。

The main contribution in this thesis is Piecewise-Lyapunov-Function-
Based Switching Fuzzy Observer with non-quadratic stability for continuous
fuzzy system. At first, we consider several non-quadratic Lyapunov
function with form designed as
V (x) = xTP(x)x = 1
g(g􀀀1)xT∇xxV (x)x.
Then, we combine these Lyapunov functions into one Piecewise-
Lyapunov-Function by the parameter, , and design the Switching Observer
by using the crossing point forming Piecewise-Lyapunov-Function.
At the same time, we investigate the stable condition with different type
fuzzy system.
In numerical simulation, we solve for Piecewise-Lyapunov-Function-
Based Switching Fuzzy Observer with sum-of-squares approach.

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