KSME Journal

, Volume 9, Issue 3, pp 344–350 | Cite as

Design of disturbance decoupled bilinear observers

  • Kyongsu Yi


An observer structure for bilinear systems is formulated such that the estimation error is independent of unknown external disturbances. The sufficient conditions for the existence of a stable bilinear observer are described. The proposed observer is applied to estimate the tire force in a vehicle semi-active suspension problem.

Key Words

Bilinear Observer Bilinear Systems Disturbance Stability Semi-Active Suspensions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bhattacharyya, S. P., 1978, “Observer Design for Linear System with Unknown Inputs,”IEEE Trans. on Auto. Contr., Vol. AC-23(3), pp. 483–484.MATHCrossRefMathSciNetGoogle Scholar
  2. Derese, I., Stevens, P. and Noldus, E., 1979, Observers for Bilinear Systems with Bounded Input,”Int. Journal Systems Science, Vol. 10, No. 6, pp. 649–668.MATHCrossRefMathSciNetGoogle Scholar
  3. Derese, I. A. and Noldus, E. J., 1981, “Existence of Bilinear State Observers for Bilinear Systems,”IEEE Trans. on Auto. Contr., Vol. AC-26, pp. 590–592.MATHCrossRefMathSciNetGoogle Scholar
  4. Fairman, F. W., Mahil, S. S. and Luk, L., 1984, “Disturbance Decoupled Observer Design Via Singular Value Decomposition,”IEEE Trans. on Automatic Control, Vol. AC-29(1), pp. 84–86.MATHCrossRefGoogle Scholar
  5. Funahashi, Y., 1978, “A Class of State Observers for Bilinear Systems,”Int. Journal Systems Science, Vol. 9, No. 1, pp. 1199–1205.MATHCrossRefMathSciNetGoogle Scholar
  6. Funahashi, Y., 1979, “Stable state Estimator for Bilinear Systems,”Int. J. Control, Vol. 29, No. 2, pp. 649–668.CrossRefMathSciNetGoogle Scholar
  7. Grasselli, O. M. and Isidori, A., 1981, “An Existence Theorem for Observers for Billinear Systems,”IEEE Trans. on Auto. Contr., Vol. AC-26, pp. 1299–1301.MATHCrossRefMathSciNetGoogle Scholar
  8. Hac, A., 1989, “Design of Disturbance Decoupled Observer for Bilinear Systems,”ASME Winter Annual Meeting, San Francisco, California, December 1989.Google Scholar
  9. Hara, S. and Furuta, K., 1976, “Minimal Order State Observers for Bilinear Systems,”International Journal of Control, Vol. 24(5), pp. 705–718.MATHCrossRefMathSciNetGoogle Scholar
  10. Hsu, C. S. and Karanam, V. R., 1981, Observer Design of Bilinear Systems,” 24th Midwest Symposium on Circuits and Systems, Western Periodicals, pp. 761–764.Google Scholar
  11. Kimbrough, S. S., 1984, “Regulators for Bilinear Systems,”Ph. D. Thesis, the Dept. of Mechanical Engineering, UCLA.Google Scholar
  12. Kobayashi, N. and Nakamizo, T., 1982, “An Observer Design for Linear Systems with Unknown Inputs,”Int. Journal of Control, Vol. 35, No. 4, pp. 605–619.MATHCrossRefMathSciNetGoogle Scholar
  13. Safonov, M. G. and Athans, M., 1978, “Robustness and Computational Aspects of Nonlinear Stochastic Estimators and Regulators,”IEEE Trans. Aut. Cont., Vol. AC-23, No. 4, pp. 717–725.MATHCrossRefMathSciNetGoogle Scholar
  14. Williamson, D., 1977, “Observation of Billinear Systems with Application to Biloggical Control,”Automatica, Vol. 13, pp. 243–254.MATHCrossRefGoogle Scholar
  15. Yi, K. and Hedrick, J. K., 1989, “Active and Semi-Active Heavy Truck Suspensions to Reduce Pavement Damage,” SAE Paper No. 892486.Google Scholar
  16. Yi, K. and Hedrick, K., 1993, “Dynamic Tire Force Control by a Semi-Active Suspension,”ASME Trans. J. of Dyn. Syst., Meas. and Control. Vol. 115, No. 3, pp. 465–474.MATHCrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 1995

Authors and Affiliations

  • Kyongsu Yi
    • 1
  1. 1.School of Mechanical, PrecisionDesign and Automotive Engineering Hanyang UniversitySeoulKorea

Personalised recommendations