Skip to main content
Log in

On observability of singular systems

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript


Concepts of observability and strong observability for singular systems are introduced and characterized geometrically in terms of the system matrices without using the Weierstrass decomposition. Duality relations between observability and controllability and that between reachability and strong observability are established. A canonical form for the action of the output injection group on the set of observable systems is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. Malabre, M., More geometry about singular systems, Rapport Interne No. 1.87, LANENSM, Nantes, 1987 (a shorter version is inProc. 26th IEEE CDC, pp. 1138–1139, Los Angeles, CA, December 1987).

  2. Cobb, J. D., Controllability, observability, and duality in singular systems,IEEE Trans. Automat. Control, Vol. 29, No. 12, pp. 1076–1082, December 1984.

    Google Scholar 

  3. Yip, E. L., and Sincovec, E. F., Solvability, controllability, and observability of continuous descriptor systems,IEEE Trans. Automat. Control, Vol. 26, No. 3, pp. 702–707, June 1981.

    Google Scholar 

  4. Verghese, G. C., Levy, B. C., and Kailath, T., A generalized state-space for singular systems,IEEE Trans. Automat. Control, Vol. 26, No. 4, pp. 811–831, August 1981.

    Google Scholar 

  5. Rosenbrock, H. H., Structural properties of linear dynamical systems,Internat. J. Control, Vol. 20, No. 2, pp. 191–202, 1974.

    Google Scholar 

  6. Banaszuk, A., Kociecki, M, and Przykuski, K. M., Remarks on duality between observation and control for implicit linear discrete-time systems,Proc. IFAC Workshop on System Structure and Control, pp. 257–260, Prague, Czechoslovakia, September 1989.

  7. Banaszuk, A., Kociecki, M., and Przyluski, K. M., Remarks on controllability of implicit linear discrete-time systems,Systems and Control Lett., Vol. 10, pp. 67–70, 1988.

    Google Scholar 

  8. Özçaldiran, K., and Lewis, F. L., Some generalized notions of observability,Proc. 29th CDC, pp. 3635–3639, Honolulu, HI, December 1990.

  9. Özçaldiran, K., Control of Descriptor Systems, Ph.D. Thesis, School of Electrical Engineering, Georgia Institute of Technology, June 1985.

  10. Özçaldiran, K., and Lewis, F. L., On the regularizability of singular systems,IEEE Trans. Automat. Control, Vol. 35, no. 10, pp. 1156–1160, October 1990.

    Google Scholar 

  11. Özçaldiran, K., A complete classification of controllable singular systems, submitted, 1989.

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Baser, U., Özçaldiran, K. On observability of singular systems. Circuits Systems and Signal Process 11, 421–430 (1992).

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: