多重時間延遲之奇異擾動系統的穩定性分析及控制器設計

Abstract

本文探討了三種不同類別的具有多重時間延遲之奇異性擾動系統。第一種 類別為線性非時變多重時間延遲之奇異性擾動系統，對於這些系統，我們 根據H-infinity範數來求得一個與時間延遲相關的奇異擾動參數esilon之 穩定上限值。而第二種類別為非線性多重時間延遲之奇異性擾動系統，在 這些系統的研究上，我們首先針對無時間延遲的非線性奇異性擾動系統來 設計一個動態輸出回授控制器。然後，根據積分流形的方法，我們對非線 性多重時間延遲之奇異性擾動系統來設計一個狀態回授控制器，使得整個 閉迴路系統的軌跡，從任何狀態的初始值開始延著積分流形以指數的形式 及某個設定的收斂速率收斂到原點。最後本文討論第三種類別－離散線性 非時變多重時間延遲之奇異性擾動系統－的控制器設計之問題，我們首先 對離散線性非時變無時間延遲之奇異性擾動系統提出一個新的狀態回授控 制器設計的方法，使得整個受控系統是D-穩定的。接下來，我們對離散線 性非時變多重時間延遲之奇異性擾動系統提出一個有效的法則來求得奇異 擾動參數的D-穩定上限值。 In this dissertation, the stability analysis and control design for three various classes of multiple time-delay singularly perturbed systems are investigated. The first class of systems is the linear time-invariant (LTI) multiple time- delay singularly perturbed systems. For these systems, a delay-dependent stability bound of singular perturbation parameter esilon is provided in terms of the H-infinity norm. Then, the nonlinear multiple time-delay singularly perturbed systems are considered as the second class of systems. For these systems, we first design the dynamic output feedback control for the nonlinear singularly perturbed systems without time delay, and then the integral manifold approach is used to design the state feedback control for the nonlinear singularly perturbed systems with mutiple time delays such that the trajectories of the closed-loop systems, starting from any initial states, are steered along the integral manifold to the origin exponentially, with some guaranteed convergence rate. Finally, the third class of systems, the discrete LTI multiple time-delay singularly perturbed systems, is examined. For these systems, we first propose a new approach for separate design of the state feedback control to make the controlled discrete singularly perturbed system without time delay D- stable. Subsequently, an efficient algorithm for finding the D-stabilization bound of esilon is proposed for discrete multiple time-delay singularly perturbed systems.