與現有文獻上所提出的線性矩陣不等式條件相比，本論文藉由投影引理對於連續系統上的混合 H2/H_inf 控制提出一個比較不保守的線性矩陣不等式條件。相同的技巧也被應用到具有非時變凸形不確定量之連續系統的混合 H2/H_inf 控制。同時提供兩個數值模擬的例子以突顯論文中所提出的線性矩陣不等式條件帶來的改進。最後，本論文嘗試用投影引理來處理具有時變凸形不確定量之連續系統的穩定性分析與設計。

By exploiting the Projection Lemma, this thesis provides less conservative LMI-like conditions for mixed H2 and H_inf control of continuous-time systems than those appeared in the current literature. The same technique has been extended to problems with time-invariant polytopic uncertainties. Numerical examples are illustrated to show improvement of the proposed results. Finally, an attempt is made to apply the Projection Lemma to stability analysis and design of systems with time-varying polytopic uncertainties.

Contents
1 Introduction 1
2 Preliminary 4
2.1 Matrix properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Extended H2 performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Extended H_inf performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Extended H2 and H_inf Control 13
3.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Static state-feedback synthesis . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Dynamic output-feedback synthesis . . . . . . . . . . . . . . . . . . . . . . 17
3.4 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Extended H_inf and H2 Control with Time-Invariant Polytopic Uncertainties 27
4.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Static state-feedback synthesis . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Stability Analysis and Design of Systems with Time-Varying Polytopic Uncertainties 34
5.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.2 Static state-feedback synthesis . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3 Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6 Conclusion 42
Appendix A 43
Bibliography 44

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