Journal of the Institute of Electronics Engineers of Korea SC (전자공학회논문지SC)

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A Poof of Utkin's Theorem for a SI Uncertain Linear Case

Utkin 정리의 단일입력 불확실 선형 시스템에 대한 증명

  • Lee, Jung-Hoon (Dept of Control & Instrum. Eng., Gyeongsang National University)
  • 이정훈 (국립경상대학교 제어계측공학과, ERI)
  • Received : 2011.01.24
  • Published : 2011.11.25
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Abstract

In this note, a proof of Utkin's theorem is presented for SI(Single input) uncertain linear systems. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods is proved clearly and comparatively for SI uncertain linear systems. With respect to the sliding surface transformation, the equation of the sliding mode i.e., the sliding surface is invariant. The control inputs by the two transformation methods both have the same gains. By means of the two transformation methods, the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified.

본 연구에서는 불확실 단일 입력 시스템의 경우에 대하여 Utkin 정리의 증명을 제시한다. 소위 두가지의 대각화 방법(Diagonalization Method)이라 불리는 Utkin 정리의 두 변환 방법에 대한 불변 정리를 비교적으로 분명히 증명한다. 슬라이딩모드의 수식 즉 슬라이딩 면은 두가지 대각화 변환에 대하여 변화 없고 두 인가된 제어입력은 같은 이득을 갖는다. 두가지 대각화 방법에 의하여 같은 결과를 얻는다. 설계 예와 시뮬레이션 연구를 통하여 제안된 결과의 효용성을 입증한다.

Keywords

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