Delay-Dependent Robust Stabilization for Time-varying Delay Uncertain Systems with Actuator Saturation

具飽和致動器時延系統之時延相關強健穩定化準則

劉柄麟(Pin-Lin Liu)

《建國科大理工期刊》 30卷2期 (2011/04) Pp. 19-37

https://doi.org/10.6995/JSECTU.201104.0019

摘要

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針對具飽和參數推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園。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園使得系統仍為漸近穩定。

關鍵字

牛頓萊布尼茲公式 ； 線性矩陣不等式 ； 時延相關

並列摘要

In this paper, the problems of stabilization criteria for a class of linear time-varying 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.

並列關鍵字

Leibniz-Newton formula ； linear matrix inequality ； time delay ； delay-dependence