Electron. J. Diff. Eqns., Vol. 2001(2001), No. 67, pp. 1-13.

Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces

Vu Ngoc Phat

Abstract:
This paper studies the stabilization of the infinite-dimensional linear time-varying system with state delays
$$\dot x = A(t)x + A_1(t)x(t-h)+B(t)u\,.$$
The operator $A(t)$ is assumed to be the generator of a strong evolution operator. In contrast to the previous results, the stabilizability conditions are obtained via solving a Riccati differential equation and do not involve any stability property of the evolution operator. Our conditions are easy to construct and to verify. We provide a step-by-step procedure for finding feedback controllers and state stability conditions for some linear delay control systems with nonlinear perturbations.

Submitted August 16, 2001. Published October 19, 2001.
Math Subject Classifications: 93D15, 93B05, 34K20.
Key Words: Stabilization, time-varying, delay system, Riccati equation.

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Vu Ngoc Phat
School of Electrical Engineering & Telecommunications
Faculty of Engineering, University of New South Wales
Sydney 2052, Australia
e-mail: phvu@syscon.ee.unsw.edu.au
On leave from
Institute of Mathematics
P.O. Box 631, BoHo, Hanoi, Vietnam
e-mail:vnphat@thevinh.ncst.ac.vn

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