Steady Modes in Relay Control Systems With Time Delay and Periodic Disturbances

[+] Author and Article Information
E. Fridman

Department of Electrical Engineering, Tel Aviv University, Ramat-Aviv, 69978 Tel Aviv, Israele-mail: emilia@eng.tau.ac.il

L. Fridman

Chihuahua Institute of Technology, Av. Technologica 2909, A.P. 2-1549, Chihuahua, Chi, C.P. 31160, Mexicoe-mail: lfridman@platon.itch.edu.mx

E. Shustin

School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv, 69978 Tel Aviv, Israele-mail: shustin@math.tau.ac.il

J. Dyn. Sys., Meas., Control 122(4), 732-737 (Feb 18, 2000) (6 pages) doi:10.1115/1.1320443 History: Received February 18, 2000
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.


Choi,  S.-B., and Hedrick,  J. K., 1996, “Robust Throttle Control of Automotive Engines,” ASME J. Dyn. Syst., Meas. Control, 118, No. 1, pp. 92–98.
Li, X., and Yurkovitch, S., 1999, “Sliding Mode Control of System With Delayed State and Controls,” Sliding Mode and Nonlinear Control, K. D. Young and U. Ozguner, eds., Lecture Notes in Control and Information Sciences, Vol. 247, Springer, Berlin, pp. 93–108.
Bartolini,  G., Caputo,  W., Cecchi,  M., Ferrara,  A., and Fridman,  L., 1997, “Vibration Damping in Elastic Robotic Structure via Sliding Modes,” J. of Robotic Systems, 14, No. 9, pp. 675–696.
Fridman,  L., Fridman,  E., and Shustin,  E., 1993, “Steady Modes in an Autonomous System With Break and Delay,” Differential Equations (Moscow), 29, No. 8, pp. 1161–1166.
Shustin,  E. I., Fridman,  E. M., and Fridman,  L. M., 1993, “Steady Modes in a Discontinuous Control System With Time Delay,” Pure Mathematics and Applications (Budapest), 4, pp. 59–73.
Kolmanovskii, V., and Myshkis, A., 1992, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht.
Mallet-Paret,  J., 1988, “Morse Decomposition for Delay-Differential Equation,” J. Diff. Eqns., 72, pp. 270–315.
Mallet-Paret, J., and Nussbaum, R. D., 1986, “A Bifurcation Gap for a Singularly Perturbed Delay Equation,” Chaotic Dynamics and Fractals, Vol. 2, M. F. Barnsley and S. G. Demko, eds., Academic Press, New York, pp. 263–287.
Mallet-Paret,  J., and Nussbaum,  R. D., 1992, “Boundary Layer Phenomena for Differential-Delay Equations With State-Dependent Time Lags, I,” Arch. Ration. Mech. Anal., 120, pp. 99–146.
Nussbaum, R. D., 1979, “Periodic Solution of Nonlinear Autonomous Functional-Differential Equations,” Functional Differential Equations and Approximations of Fixed Points, Lecture Notes in Mathematics, Vol. 730, Springer-Verlag, Berlin, pp. 283–325.
Peters,  H., 1980, “Comportement Chaotique d’une Équation Differentielle Retardée,” C. R. Acad. Sci. Paris, 290, pp. 1119–1122.
Saupe,  D., 1983, “Global Bifurcation of Periodic Solutions to Some Autonomous Differential Delay Equations,” Appl. Math. Comput., 13, pp. 185–211.
Akian, M., and Bliman, P.-A., 1998, “On Super High Frequencies in Discontinuous 1-st Order Delay-Differential Equation,” Proceedings, 6th IEEE Mediterranean Conference on Control and Systems, Alghero, Italy.
Dix,  J. G., 1998, “Infinite Frequency Solutions to Discontinuous Control Systems With Different Delay,” Israel J. Math., 106, pp. 165–176.
Nussbaum, R., and Shustin, E., 1998, “Nonexpansive Periodic Operators in l1 With Applications in a Discontinuous Dynamical System With Time Delay,” Preprint, Rutgers University.
Shustin,  E., 1995, “Super-High-Frequency Oscillations in a Discontinuous Dynamic Delay System,” Israel J. Math., 90, pp. 199–219.
Walther,  H.-O., 1981, “Density of Slowly Oscillating Solutions of ẋ(t)=−f(x(t−1)),” J. Math. Anal. Appl., 79, pp. 127–140.
Walther,  H.-O., 1991, “An Invariant Manifold of Slowly Oscillating Solutions for ẋ(t)=−μx(t)+f(x(t−1)),” J. Reine Angew. Math., 414, pp. 67–112.
Nitecki, Z., 1971, Differential Dynamics, M.I.T. Press, Cambridge.
Utkin, V. I., 1992, Sliding Modes in Optimization and Control Problems, Springer Verlag, Berlin.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In