P. Niamsup & V. N. Phat
Abstract:
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 | |
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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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