無漂流擾動系統之穩定化

Abstract

在本論文中，我們探討非線性無漂流項系統的漸近穩定性與強健控制。根 據廖德誠博士與梁耀文先生在1993年所發表的研究成果，我們獲得較實用 的系統漸近穩定與強健穩定性之條件。此乃經由定義一與系統動態相關的 實函數，然後，推論此函數在原點具有絕對最小值與系統穩定的對等性而 獲得。此一方法的優點是我們可以運用微積分的技巧求得此函數在原點是 否具有絕對最小值來保證系統之漸近穩定。應用同樣的方法並建立適當的 李亞普諾夫函數(Lyapunov function) 我們獲得保證受擾動系統(Pe- rturbed System) 具有強健(Robust)特性的條件。另外，我們重新證明 Brockett先生在1983所提出的無漂流項系統穩定性的充分且必要條件。最 後，我們探討齊階雙線性系統(Homogeneous Bilinear Systems)的穩定性 條件。 Issues of asymptotic stabilization and robust control of the nonlinear driftless systems are presented in this thesis. Based on the works of D. -C. Liaw and Y. -W. Liang(1993), practically asymptotic stabilizability conditions and robust stabilizability conditions are obtained. This is achieved by defining a real_valued function in terms of system dynamics and then deduce the equivalence of system stability and the minimization of the ined real-valued functions at the origin. The advantage of this process is that we can employ the technique of calculus to derive the minimization of that real- valued functions for guaranteeing system stability. Applying the same approach to construct a suitable Lyapunov function, we derive conditions for guaranteeing robust property of perturbed system. Moreover, we reprove Brockett's necessary and sufficient condition on driftless system. Finally, the stabilizability of homogeneous bilinear system is also presented.