本論文旨在藉由線性矩陣不等式(LMI)與牛頓萊布尼茲公式(Leibniz-Newton
formula) 經由選擇適當之李亞普諾夫函數(Lyapunov-Krasovskii function, LKF)提
出具飽和致動器時延系統之時延相關強健穩定化準則。本論文利用最佳化演算法
設計飽和致動器迴授控制器推導出基於LMI 的控制器設計方法。引用LKF 結合
LMI 針對具飽和參數擾動時延系統遭受擾動時欲維持系統之強健穩定性時系統
所能承受擾動之強健穩定時間延遲範圍。文中舉例驗證與現有文獻結果相比較可
得較寬廣的時間延遲範圍使得系統仍為漸近穩定。

In this paper, the problems of stabilization criteria for a class of linear timevarying
delay uncertain systems with saturating actuator are derived. Based on the
Lyapunov-Krasovskii functional combining with LMI techniques and Leibniz-
Newton formula, delay-dependent stabilization criteria are derived for the existence of
a state feedback controller, which ensures asymptotic stability of the closed systems
for all admissible uncertainties. Furthermore, we try to transform the LMI feasible
problem into the equivalent generalized eigenvalue problem (GEVP). Such that the
global solution, namely the maximum upper bound on the admissible delay, can be
determine by using the LMI toolbox in Matlab. Finally, two numerical examples are
given to demonstrate the feasibility and solve the generalized eigenvalue
minimization problem (GEVP) of our proposed approach.