An Identification Procedure for Linear Continuous Time Systems with Jump Parameters

  • Carla A. Schwartz
  • Hitay Özbay
Part of the Progress in Systems and Control Theory book series (PSCT, volume 3)


We formulate an identification procedure for multi-input/ multi-output linear continuous time systems with jump parameters in the absence of observation noise. We assume that the parameters of the system depend on a Markov chain whose matrix of transition rates is unknown. We propose discrete time parameter estimation methods for the continuous time system to be identified. This includes a procedure for estimating the statistics of the Markov chain driving the parameter jumps.


Covariance SinAn 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D.D. Sworder and D.S. Chou “A survey of some design methods for random parameter systems”, Proceedings of 24 th Conference on Decision and Control, Ft. Lauderdale, 1985, pp. 894–899.Google Scholar
  2. [2]
    P.A. Ioannou, K.S. Tsakalis, A Robust Direct Adaptive Controller, IEEE Trans. Autom. Control, vol AC-31, no. 11, 1986, pp. 1033–1043.Google Scholar
  3. [3]
    R.H. Middleton, G.C. Goodwin, Adaptive Control of Time-Varying Linear Systems, IEEE Trans. Autom. Control, vol AC-33, no.2, 1988, pp. 150–155.Google Scholar
  4. [4]
    R. Johansson “Identification of continuous time systems”, Proceedings of 20 th Conference on Decision and Control, Athens, 1986, pp. 1653–1658.Google Scholar
  5. [5]
    M. Mariton “Stochastic observability of linear systems with Markovian jumps”, Proceedings of 25 th Conference on Decision and Control, Athens, 1986 pp. 2208–2209.Google Scholar
  6. [6]
    W. Feller An Introduction to Probability Theory and its Applications volume one, John Wiley, 1950.Google Scholar
  7. [7]
    P.E. Caines and H.F. Chen “Optimal adaptive LQG control for systems with finite state process parameters”, IEEE Transactions on Automatic Control 1985, pp. 185–189Google Scholar
  8. [8]
    M. Mariton and P. Bertrand “Comportement asymptotic de la commande pour les systèmes linéaires à saut markoviens” C. R. Acad. Sci. Paris vol. 301, 1985, pp. 683–686.Google Scholar
  9. [9]
    G.C. Goodwin and K.S. Sin Adaptive Filtering Prediction and Control, Prentice-Hall 1984.Google Scholar
  10. [10]
    P.E. Caines, Linear Stochastic Systems, Wiley, 1988.Google Scholar
  11. [11]
    T.R. Fortescue, L.S. Kershenbaum, and B.E. Ydstie “Implementation of self tuning regulators with variable forgetting factors” Automatica, pp. 831–835.Google Scholar
  12. [12]
    S. Barnett Matrices in Control Theory, Van Nostrand Reinhold, 1971.Google Scholar
  13. [13]
    W. Feller An Introduction to Probability Theory and its Applications volume two, John Wiley, 1970.Google Scholar
  14. [14]
    M. Millnert, “Identification of ARX models with markovian parameters”, Int. J. Control, 1987, vol 45, no 6, pp. 2045–2058.CrossRefGoogle Scholar
  15. [15]
    C. Yang, P. Bertrand, M. Mariton, “A failure detection method for systems with poorly known parameters”, ICCON ′89, April 1989, Jerusalem, Isreal.Google Scholar

Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • Carla A. Schwartz
  • Hitay Özbay

There are no affiliations available

Personalised recommendations