DOI QR코드

DOI QR Code

Robust Mixed H2/H Filter Design for Uncertain Fuzzy Systems

불확실한 퍼지시스템의 견실한 혼합 H2/H 필터 설계

  • 류석환 (대구대학교 전자정보공학부) ;
  • 최병재 (대구대학교 전자정보공학부)
  • Published : 2004.08.01

Abstract

This paper deals with a robust mixed ${H_2}/{H_{\infty}}$ filter design problem for a nonlinear dynamic system modeled as a T-S fuzzy system. Integral quadratic constraints are used to describe various kinds of uncertainties of the plant. A sufficient condition for solvability is given in terms of linear matrix inequality problem which can be efficiently solved using a convex optimization technique. In order to demonstrate the Proposed method, a numerical design example is provided.

이 연구는 T-S 퍼지시스템으로 모델 되는 비선형 시스템의 견실한 혼합 ${H_2}/{H_{\infty}}$ 필터 설계문제를 취급한다. 플랜트에 포함된 다양한 종류의 불확실성을 취급하기 위하여 적분 2차 제약조건을 사용하였다. 필터 설계문제의 해가 존재할 충분조건을 볼록 최적화 기법을 사용하여 효과적으로 풀 수 있는 선형 행렬 부등식의 형태로 제시한다. 제시된 방법을 예시하기 위해서 수치 예를 보여준다.

Keywords

References

  1. L. Xie, C.E.de Souza and Y.C.Soh, "Robust Kalman filter for uncertain discrete time systems," IEEE Trans. Automatic Control, vol.39, pp.1310-1314, 1994. https://doi.org/10.1109/9.293203
  2. Y. Theodor and U. Shaked, "Robust discrete time minimum variance filtering," IEEE Trans. Signal Processing, vol.44, pp.181-189, 1996. https://doi.org/10.1109/78.485915
  3. K.A. Barbosa and C.E.de Souza, "Robust $H_2$ filtering for discrete time uncertain linear systems using parameter dependent Lyapunov functions," Proceedings of the American control conference, Anchorage, AK, May 8-10, pp.3224-3229, 2002.
  4. R.M. Palhares and P.D. Peres, "LMI approach to the mixed $H_2$/$H_{\infty}$ filtering design for discrete time uncertain systems," IEEE Trans. Aerospace and Electronic Systems, vol.37, no.1, pp.292-296, Jan. 2001. https://doi.org/10.1109/7.913689
  5. C. Tseng and B. Chen, " Fuzzy estimation for a class of nonlinear discrete time dynamic systems," IEEE Trans. Signal Processing, vol.49, no.11, pp.2605-2619, Nov. 2001. https://doi.org/10.1109/78.960407
  6. B. Chen, C. Tsai and D. Chen, "Robust $H_{\infty}$ and mixed $H_2$/$H_{\infty}$ filters for equalization designs of nonlinear communication systems : Fuzzy interpolation approach", IEEE Trans. Fuzzy Systems, vol.11, no.3, pp.384-398, Jun. 2003. https://doi.org/10.1109/TFUZZ.2003.812698
  7. A. Megretski and A. Rantzer, "System analysis via integral quadratic constraints," IEEE Trans. Automatic Control, vol.42, no.6, pp.819-830, Jun. 1997. https://doi.org/10.1109/9.587335
  8. C.W. Scherer, P. Gahinet and M. Chilali," Multi-objective output feedback control via LMI optimization", IEEE Trans. Automatic Control, Vol.42, no.7, pp.896-911, Jul., 1997. https://doi.org/10.1109/9.599969
  9. K. Tanaka, T. Ikeda and H.O. Wang,"Robust stabilization of a class of uncertain nonlinear systems via fuzzy control : Quadratic stabilizability, $H_{\infty}$ control theory and linear matrix inequalities", IEEE Trans. Fuzzy Systems, vol.4, no.1, pp.111-13, Feb., 1996.
  10. S. Boyd, L. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, Philadelphia, 1994.
  11. J. C. Geromel, "Optimal linear filtering under parameter uncertainty", IEEE Trans. on Signal Processing, vol.47, no.1, pp.168-175, January, 1999. https://doi.org/10.1109/78.738249
  12. H.D. Tuan, P. Apkarian and T. Q. Nguyen, "Robust filtering for uncertain nonlinearly parameterized plants", IEEE Trans. on Signal Processing, vol.51, no.7, July, 2003.