Robust Exponential Stability Analysis and Controller Design of Continuous-time Structured Uncertain Systems

連續時間結構化不確定系統之強健指數型穩定性分析與控制器設計

楊錫凱(Shyi-Kae Yang)

《中國機械工程學刊》 30卷4期 (2009/08) Pp. 357-361

https://doi.org/10.29979/JCSME.200908.0010

摘要

本文探討具結構化不確定性系統的強健指數型穩定性分析與控制器設計問題。首先利用Lyapunov二次型穩定條件，將不確定系統達到指數型穩定的判斷推導成為一個LMI最佳化問題的求解，並將問題延伸推導得到一個具LMI條件的GEVP，可以直接計算得到不確定系統動態的指數衰減率；最後針對一給定之不確定系統，提出基於LMI最佳化問題的控制器設計條件，可以很容易的設計出該不確定系統滿足強健指數穩定的狀態回授增益。

並列摘要

This study considers the robust exponential stability analysis and controller design of continuous-time structured uncertain systems. Utilizing a Lyapunov quadratic stability criterion, the problem of deriving the conditions which ensure the uncertain system achieves robust exponential stability is formulated as a linear matrix inequality (LMI) optimization problem. The problem of determining the robust exponential decay rate of the dynamics of the uncertain system is then formulated as a generalized eignevalue problem (GEVP) subject to LMI constraints. Finally, a stabilizing condition for the uncertain system is proposed, and a robust controller is designed to enforce the pre-specified exponential decay dynamics.

並列關鍵字

exponential stability ； linear matrix inequality ； robust controller design ； structured uncertainty