Abstract
This paper describes a way of designing a piecewise-linear system with discretely adjustable parameters (a hybrid linear system) in which we can switch the transfer matrix of the system without causing a discontinuity (a bump) in the system output. This is similar to the result that we could achieve by doing a bumpless transfer between multiple linear systems, but the order of a hybrid linear system will typically be much less than the combined order of the multiple systems that realize the same set of transfer matrices.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
R. Alur, T. A. Henzinger, and E. D. Sontag (eds.), Hybrid Systems III. Verification and Control, Lecture Notes in Computer Science 1066, Springer, 1996.
A. B. Arehart and W. A. Wolovich, “A nonlinear programming procedure and a necessary condition for the simultaneous stabilization of 3 or more linear systems,” in Proceedings of the 34th IEEE Conference on Decision and Control, pp. 2631–2632, Dec. 1995.
A. B. Arehart and W. A. Wolovich, “Bumpless switching controllers,” in Proceedings of the 35th IEEE Conference on Decision and Control, pp. 1654–1655, Dec. 1996.
V. Blondel, Simultaneous Stabilization of Linear Systems. Springer, 1994.
Y.-K. Chin, Theoretical and Computational Considerations for Finite Time Interval System Identification Without Initial State Estimation. PhD thesis, Brown U., 1977.
S. F. Graebe and A. Ahlén, “Bumpless transfer,” in The Control Handbook, W. S. Levine (ed.), pp. 381–388, CRC, Dec. 1995.
R. L Grossman, A. Nerode, A. P. Ravn, and H. Rischel (eds.), Hybrid Systems, Lecture Notes in Computer Science 736, Springer, 1993.
R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, “Introduction,” in [7], pp. 1–3, Springer, 1993.
M. Lemmon, J. A. Stiver, P. J. Antsaklis, “Event identification and intelligent hybrid control,” in [7], pp. 268–296, Springer, 1993.
M. Mariton, Jump Linear Systems in Automatic Control. Marcel Dekker, 1990.
MathWorks, SIMULINK User's Guide, 1992.
A. S. Morse, “Control using logic-based switching,” in Trends in Control, A. Isidori (ed.), Springer, pp. 69–114, Sept. 1995.
K. S. Narenda and S. S. Tripathi, “Identification and optimization of aircraft dynamics,” Journal of Aircraft, vol. 10, pp. 193–199, Apr. 1973.
H. S. Park, Y. S. Kim, W. H. Kwon, and S. J. Lee, “Model and stability of hybrid linear system,” in [1], pp. 424–435, Springer, 1996.
J. Seddon, Basic Helicopter Aerodynamics, AIAA Education Series, 1990.
E. D. Sontag, “Interconnected automata and linear systems: a theoretical frame-work in discrete-time,” in [1], pp. 436–448, Springer, 1996.
J. Wang and Y. Juang, “A new approach for computing the state feedback gains of multivariable systems,” IEEE Transactions on Automatic Control, vol. 40, pp. 1823–1826, Oct. 1995.
W. A. Wolovich, Linear Multivariable Systems. Springer, 1974.
W. A. Wolovich, Automatic Control Systems: Basic Analysis and Design. Saunders, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arehart, A.B., Wolovich, W.A. (1997). Bumpless switching in hybrid systems. In: Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems IV. HS 1996. Lecture Notes in Computer Science, vol 1273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031552
Download citation
DOI: https://doi.org/10.1007/BFb0031552
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63358-7
Online ISBN: 978-3-540-69523-3
eBook Packages: Springer Book Archive