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

The Institute of Electronics and Information Engineers (대한전자공학회)
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Robust $H_{\infty}$ filtering for discrete-time polytopic uncertain systems

이산시간 폴리토프형 불확실성 시스템의 견실 $H_{\infty}$ 필터링

  • Kim, Jong-Hae (Division of Electronics, Information and Communication Engineering, Sunmoon University) ;
  • Oh, Do-Chang (Division of Information and Technology, Konyang University) ;
  • Lee, Kap-Rai (Department of Information Science, Pyongtaek University)
  • 김종해 (鮮文大學校 電子情報通信工學部) ;
  • 오도창 (建陽大學校 IT學部) ;
  • 이갑래 (平澤大學校 情報科學部)
  • Published : 2002.09.01
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Abstract

The design method of robust $H_{\infty}$ filtering for discrete-time uncertain linear systems is investigated in this paper. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytope type. The objective is to design a stable robust $H_{\infty}$ filter guaranteeing the asymptotic stability of filtering error dynamics and present an $L_2$ induced norm bound analytically for the modified $H_{\infty}$ performance measure. The sufficient condition for the existence of robust $H_{\infty}$ filter and the filter design method are established by LMI(linear matrix inequality) approach, which can be solved efficiently by convex optimization. The proposed algorithm is checked through an example.

본 논문에서는 볼록 한계 불확실성(convex bounded uncertainty)을 가지는 이산시간 선형 시스템의 견실 $H_{\infty}$ 필터 설계 알고리듬을 제안한다. 다루고 있는 파라미터 불확실성은 폴리토프형(polytope type) 볼록 한계를 가지는 형태이다. 본 논문의 목적은 필터링 오차 시스템의 점근 안정성(asymptotic stability)과 변형한 성능지수의 유도 $L_2$ 노옴($L_2$ induced norm) 한계치를 해적적으로 제시하는 안정한 견실 $H_{\infty}$ 필터를 설계하는 것이다. 견실 $H_{\infty}$ 필터가 존재할 충분조건과 필터 설계 방법은 볼록 최적화 기법에 의하여 효과적으로 해를 구하는 선형행렬부등식 방법에 의하여 제시한다. 제안한 알고리듬의 타당성은 예제를 통하여 확인한다.

Keywords

References

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