基於許多優異的特性，順滑模態控制理論在強健控制領域中已引起廣泛注意，其發展在近幾十年間日趨成熟。其特有的優異性能是建立於理想順滑模態發生的條件下，亦即當系統狀態近入順滑模態時，系統對於外擾或不確定性具有高度強健性。也因此，順滑模態也被廣泛地應用於系統狀態觀測器之設計，順滑模態觀測器仍保有順滑模態的良好特性，系統在順滑模態中將不受匹配式外擾或系統不確定性之影響。本文提出一強健順滑模態觀測器架構，並應用於混沌系統之同步化問題，對於不同系統之條件，皆具有良好的精度，並可針對系統參數進行調校。然而在傳統設計方法中，對於非匹配式外擾及系統不變零點皆有所限制條件，雖然此舉可使設計過程更為簡單明瞭，但會大幅降低其可行性及應用面，在實際應用中，非匹配式外擾將會影響其估測精度甚至使系統不穩定，因此，本文也將針對具有非匹配式外擾之系統進行分析，並考慮不穩定的不變零點所帶來之影響，透過用性矩陣不等式方法進行參數最佳化，使系統在穩定條件下達到最佳估測效能。最後，將應用此觀測器於機械系統控制之設計。

Due to its distinct feature and robustness heritage, the sliding mode control theory receives wide attention in control system research and applications. Its distinct properties achieved by discontinuous switching control action are established when the ideal sliding motion takes place. The concept of sliding mode control has extended to the problem of state estimation known as the sliding mode observer, which possesses the merits of sliding mode dynamics. When system attains to the sliding surface, the system dynamics are totally independent of the matched uncertainties or disturbances called the invariance property. This dissertation synthesizes a sliding mode observer scheme, and it applies to a 4D chaotic system under different conditions. This shows that the observer has satisfactory performance and can updates the system parameters under specific assumptions. In addition, the systems with unstable invariant zeros and mismatched uncertainties are considered. It reveals that the mismatched uncertainties will degrade the estimation accuracy, and even result in system instability. The proposed sliding mode observer guarantees the stability, and maintains the superior performance with the observer gains optimized by the LMIs technique. The robust observer is also applied to the control of a mechanical system to demonstrate the feasibility and advantages of the proposed design scheme.

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