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

The Institute of Electronics and Information Engineers (대한전자공학회)
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Dynamic Stabilization for a Nonlinear System with Uncontrollable Unstable Linearization

제어불가능 불안정 선형화를 가지는 비선형 시스템에 대한 다이나믹 안정화

  • Seo, Sang-Bo (ASRI, School of Electrical Engineering, Seoul National University) ;
  • Shim, Hyung-Bo (ASRI, School of Electrical Engineering, Seoul National University) ;
  • Seo, Jin-Heon (ASRI, School of Electrical Engineering, Seoul National University)
  • Published : 2009.07.25
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Abstract

In this paper, we design a dynamic state feedback smooth stabilizer for a nonlinear system whose Jacobian linearization may have uncontrollable mode because its eigenvalues are on the right half-plane. After designing an augmented system, a dynamic exponent scaling and backstepping enable one to explicitly design a smooth stabilizer and a continuously differentiable Lyapunov function which is positive definite and proper. The convergence of the designed controller is proved by the new notion 'degree indicator'.

본 논문에서 우리는 비선형 시스템에 대한 다이나믹 스무스 상태 궤환 안정화기를 설계한다. 이 시스템은 우반평면에 고유값이 존재함으로 제어불가능 모드를 가질 수 있다. 이 시스템을 지수적으로 안정화하기 위해서 우리는 추가 다이나믹스를 고려한 다이나믹 제어기를 제안한다. 추가 다이나믹스의 설계 후에 다이나믹 차수 보정법과 역진기법을 이용하여 안정화기와 미분 가능, positive definite, proper인 리아푸노프 함수를 설계한다. 설계된 제어기의 수렴성은 차수 지표자라는 새로운 개념의 도입으로 증명될 것이다.

Keywords

References

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