Abstract
We study continuous-time switched linear systems with unobserved and exogenous mode signals. We analyze the observability of the initial state and initial mode under arbitrary switching, and characterize both properties in both the autonomous and non-autonomous cases.
This work was supported by NSF CAREER Grant 0132716.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Babaali, M., Egersted, M.: Observability of switched linear systems. In: Alur, R., Pappas, G. (eds.) Hybrid Systems: Computation and Control, pp. 48–63. Springer, Heidelberg (2004)
Balluchi, A., Benvenuti, L., Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L.: Observability for hybrid systems. In: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HW (December 2003)
Bemporad, A., Ferrari-Trecate, G., Morari, M.: Observability and controllability of piecewise affine and hybrid systems. IEEE Transactions on Automatic Control 45(10), 1864–1876 (2000)
Campbell, S.L., Meyer, C.D.J.: Generalized Inverses of Linear Transformations. Dover, New York (1991)
Collins, P., van Schuppen, J.H.: Observability of piecewise-affine hybrid systems. In: Ser. Hybrid Systems: Computation and Control. Springer, Heidelberg (2004)
Costa, E.F., do Val, J.B.R.: On the detectability and observability of discrete-time Markov jump linear systems. In: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, December 2000, pp. 2355–2360 (2000)
De Santis, E., Di Benedetto, M.D., Pola, G.: On observability and detectability of continuous-time linear switching systems. In: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HW (December 2003)
Ezzine, J., Haddad, A.H.: Controllability and observability of hybrid systems. International Journal of Control 49(6), 2045–2055 (1989)
Ferrari-Trecate, G., Gati, M.: Computation of observability regions for discrete-time hybrid systems. In: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HW (December 2003)
Gurvits, L.: Stabilities and controllabilities of switched systems (with applications to the quantum systems). In: Proceedings of the Fifteenth International Symposium on Mathematical Theory of Networks and Systems, August 2002, Univ. Notre Dame (2002)
Hwang, I., Balakrishnan, H., Tomlin, C.: Observability criteria and estimator design for stochastic linear hybrid systems. In: Proceedings of the IEE European Control Conference, Cambridge, UK (September 2003)
Ji, Y., Chizeck, H.: Controllability, observability and discrete-time jump linear quadratic control. International Journal of Control 48(2), 481–498 (1988)
Juloski, A., Heemels, M., Weiland, S.: Observer design for a class of piece-wise affine systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV (December 2002)
Kailath, T.: Linear Systems. Prentice Hall, Englewood Cliffs (1980)
Mariton, M.: Stochastic observability of linear systems with markovian jumps. In: Proceedings of the 25th IEEE Conference on Decision and Control, Athens, Greece, December 1986, pp. 2208–2209 (1986)
Pappas, G.J.: Bisimilar linear systems. Automatica 39(12), 2035–2047 (2003)
Sontag, E.D.: On the observability of polynomial systems, I: Finite-time problems. SIAM Journal on Control and Optimization 17(1), 139–151 (1979)
Sontag, E.D.: Nonlinear regulation: The piecewise linear approach. IEEE Transactions on Automatic Control 26(2), 346–358 (1981)
Sun, Z., Ge, S.S., Lee, T.H.: Controllability and reachability criteria for switched linear systems. Automatica (May 2002)
Tabuada, P., Pappas, G.J.: Bisimilar control affine systems. Systems & Control Letters 52(1), 49–58 (2004)
Vidal, R., Chiuso, A., Soatto, S.: Observability and identifiability of jump linear systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, December 2002, pp. 3614–3619 (2002)
Vidal, R., Chiuso, A., Soatto, S., Sastry, S.: Observability of linear hybrid systems. In: Ser. Hybrid Systems: Computation and Control. Springer, Heidelberg (2003)
West, P.D., Haddad, A.H.: On the observability of linear stochastic switching systems. In: Proceedings of the 1994 American Control Conference, Baltimore, MD, June 1994, pp. 1846–1847 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Babaali, M., Pappas, G.J. (2005). Observability of Switched Linear Systems in Continuous Time. In: Morari, M., Thiele, L. (eds) Hybrid Systems: Computation and Control. HSCC 2005. Lecture Notes in Computer Science, vol 3414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31954-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-31954-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25108-8
Online ISBN: 978-3-540-31954-2
eBook Packages: Computer ScienceComputer Science (R0)