Abstract
The object of this paper is the estimation of stability boundaries and regions of asymptotic stability with sliding for a class of relay-control systems. The direct method of Lyapunov is used to obtain these estimates. A coordinate transformation which brings the system into a special canonical form is utilized to facilitate the stability analysis. The proposed approach to stability regions estimation is applied to a class of second-order systems and analytical expressions for stability regions are derived.
The work of these authors was supported by the School of Electrical Engineering of Purdue University, West Lafayette, IN 47907.
The work of this author was partially supported by the National Science Foundation.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
V. I. Utkin, “Sliding modes and their application in variable structure systems,” Mir Publishers, Moscow 1978.
V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Automat. Contr., Vol. AC-22, No. 2, pp. 212–222, 1977.
B. Draženović, “The invariance conditions in variable structure systems,” Automatica, Vol. 5, No. 3, pp. 287–295, 1969.
R. A. DeCarlo, S. H. Żak, and G. P. Matthews, “Variable structure control of nonlinear multivariable systems: A tutorial,” Proc. of the IEEE, Vol. 76, No. 3, pp. 212–232, 1988.
S. Weissenberger, “Stability-boundary approximations for relay-control systems via a steepest-ascent construction of Lyapunov functions,” J. of Basic Engineering, Trans. of the ASME Ser. D, Vol. 38, No. 2, pp. 419–428, 1966.
O. M. E. El-Ghezawi, A. S. I. Zinober, and S. A. Billings, “Analysis and design of variable structure systems using a geometric approach,” Int. J. Control, Vol. 38, No. 3, pp. 657–671, 1983.
H. H. Rosenbrock, “A method of investigating stability,” IFAC Proc., Basel, Switzerland, pp. 590–594, 1963.
J. R. Hewit, and C. Storey, “Comparison of numerical methods in stability analysis,” Int. J. Control, Vol. 10, No. 6, pp. 687–701, 1969.
E. J. Davison, and E. M. Kurak, “A computational method for determining quadratic Lyapunov functions for non-linear systems,” Automatica, Vol. 7, No. 5, pp. 627–636, 1971.
V. G. Borisov, and S. N. Diligenskii, “Numerical method of analysis of nonlinear systems,” Automation and Remote Control, Vol. 46, No. 11, Part 1, pp. 1373–1380, Nov. 1985.
D. N. Shields, and C. Storey, “The behavior of optimal Lyapunov functions,” Int. J. Control, Vol. 21, No. 4, pp. 561–573, 1975.
R. E. Kalman, “Lyapunov function for the problem of Luŕe in automatic control,” Proc. Nat. Acad. Sci. U.S.A., Vol. 49, pp. 201–205, Feb. 1963.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Madani-Esfahani, S.M., Hui, S., Żak, S.H. (1991). Estimation of regions of asymptotic stability with sliding for relay-control systems. In: Skowronski, J.M., Flashner, H., Guttalu, R.S. (eds) Mechanics and Control. Lecture Notes in Control and Information Sciences, vol 151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006727
Download citation
DOI: https://doi.org/10.1007/BFb0006727
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53517-1
Online ISBN: 978-3-540-46752-6
eBook Packages: Springer Book Archive