An Invariance Principle for Discontinuous Dynamic Systems With Application to a Coulomb Friction Oscillator

[+] Author and Article Information
Joaquin Alvarez, Iouri Orlov

Scientific Research and Advanced Studies Center of Ensenada, BC, Mexico, Electronics and Telecommunications Department

Leonardo Acho

Universidad Autónoma de Baja California, Unidad Ensenada, Mexico, Facultad de Ingeniería

J. Dyn. Sys., Meas., Control 122(4), 687-690 (Feb 04, 2000) (4 pages) doi:10.1115/1.1317229 History: Received February 04, 2000
Copyright © 2000 by ASME
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Branicky,  M. S., 1998, “Multiple Lyapunov functions and other analysis tools for switched and hybrid systems,” IEEE Trans. Autom. Control, 43, No. 4, pp. 475–482.
Clarke,  F. H., Ledyaev,  Y. S., Sontag,  E. D., and Subbotin,  A. I., 1997, “Asymptotic controllability implies feedback stabilization,” IEEE Trans. Autom. Control, 42, No. 10, pp. 1394–1407.
Filippov, A. F., 1988, Differential Equations with Discontinuous Right-Hand Sides, Kluwer Academic, Publishers, Dordrecht.
Johansson,  K. H., Rantzer,  A., and Astrom,  K. J., 1999, “Fast switches in relay feedback systems,” Automatica, 35, pp. 539–552.
Skafidas,  E., Evans,  J. R., Savkin,  A. V., and Petersen,  I. R., 1999, “Stability results for switched controller systems,” Automatica, 35, pp. 553–546.
Utkin, V. I., 1992, Sliding Modes in Control Optimization, Springer Verlag, Berlin.
Michel, A. N., and Wang, K., 1995, Qualitative Theory of Dynamical Systems, the Role of Stability Preserving Mappings, Marcel Dekker, New York.
Berghuis,  H., and Nijmeijer,  H., 1993, “Global regulation of robots using only position measurements,” Syst. Control Lett., 21, pp. 289–293.
Hahn, W., 1967, Stability of Motion, Springer, Berlin.
Henry, D., 1981, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., Springer-Verlag, Berlin.


Grahic Jump Location
Position (solid line) and velocity (dotted line) of the enforced oscillator
Grahic Jump Location
Phase portrait of the observer error dynamics
Grahic Jump Location
One-degree-of-freedom mechanical oscillator
Grahic Jump Location
Phase portrait of the unforced oscillator



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