Electron. J. Diff. Eqns., Vol. 2000(2000), No. 11, pp. 1-17.

Asymptotic stability of nonlinear control systems described by difference equations with multiple delays

P. Niamsup & V. N. Phat

In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Holder-type assumptions on the perturbing function, and show a Gronwall-type inequality for difference equations with delay. We prove that a nonlinear control system can be stabilized if its linear control system can be stabilized. Some examples are included in the last part of this paper.

Submitted October 19, 1999. Published February 1, 2000.
Math Subject Classifications: 93D20, 34K20, 49M70.
Key Words: Stability, difference equations, nonlinear control systems, Gronwall inequality, Holder condition, multiple delay.

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  Piyapong Niamsup
Department of Mathematics, Chiangmai National University
Chiangmai 50200, Thailand
e-mail scipnmsp@cmu.chiangmai.ac.th
Vu Ngoc Phat
Institute of Mathematics
National Center for Sciences and Technology
P.O. Box 631 Bo Ho, 10.000 Hanoi, Vietnam
e-mail: vnphat@hanimath.ac.vn
e-mail: phvu@syscon.ee.unsw.edu.au (updated March 28, 2001)

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