LMI Parameterization of Lineny Sliding Surfaces for Mismatched Uncertain Systems

정합조건을 만족시키지 않는 불확실한 시스템을 위한 선형 슬라이딩 평면의 LMI 매개변수화

  • Published : 2005.11.01


In this paper, we consider the problem of designing sliding surfaces fur a class of dynamic systems with mismatched uncertainties in the state space model. In terms of LMIs, we give necessary and sufficient conditions fir the existence of a linear sliding surface such that the reduced order sliding mode dynamics is asymptotically stable and completely independent of uncertainties. We parameterize all such linear sliding surfaces by using the solution to the given LMI conditions. And, we consider the problem of designing linear sliding surfaces guaranteeing pole placement constraints or $H_2/H_infty$ performances. Finally, we give a design example in order to show the effectiveness of our method.


  1. V. I. Utkin, 'Variable Structure Systems with Sliding Modes', IEEE Trans. Automat. Contr., vol. AC-22, No.2, pp. 212-222, 1977
  2. V. I. Utkin and K D. Yang, 'Methods for constructing discontinuity planes in multidimensional variable structure systems,' Autom remote Contr., vol. 39, pp. 1466-1470, 1978
  3. C. Edwards and S. K. Spurgeon, 'Linear matrix inequality methods for designing sliding mode output feedback controllers,' lEE Proc.-Control Theory Appl., vol. 150, pp. 539-545, 2003
  4. K.-S. Kim and Y. Park, 'Parametric approaches to sliding mode design for linear multivariable systems,' Int. J. Control, Automation, and Systems, vol. 1, pp. 11-18, 2003
  5. K.-S. Kim, Y. Park, and S.-H. Oh, 'Robust sliding modes design for parametric uncertain systems:a Riccati approach,' Automatica, vol. 34, pp. 1015-1020, 2000.
  6. C. Edwards, S. K. Spurgeon, and A. Akoachere, 'Slding mode output feedback controller design using linear matrix inequalities,' IEEE Trans. Automat. Contr., vol. 46, pp. 115-119, 2001
  7. 최한호, '불확실성이 매칭조건을 만족시키지 ?는 선형 시스템을 위한 슬라이딩 평면 설계 방법,' 제어자동화시스템공학논문지, 제9권, 11호, pp. 861-867, 2003
  8. C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and Its Applications, Wiley, 1971
  9. S. Boyd, L. EIGhaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994
  10. Chilali, M. and Gahinet, P., 1996, 'Desgin with Pole Placement Constraints : An LMI Approach,' IEEE Trans on Automatic Control, Vol. 41 (3), pp. 358-369
  11. L. Keel, S. P. Bhattacharyya, and J. W. Howze, 'Robust control with structured perturbations,' IEEE Trans. Automat. Contr., vol. 33, pp. 68-78, 1988