IJPAM: Volume 65, No. 1 (2010)

THE SUFFICIENT CONDITIONS FOR STABILITY OF
LINEAR TIME-VARYING SYSTEMS WITH STATE DELAYS

Kreangkri Ratchagit
Faculty of Science
University of Maejo
Chiang Mai, 50290, THAILAND
e-mail: kreangkri@mju.ac.th


Abstract.This paper studies the stabilization of the infinite-dimensional linear time-varying system with state delays

\begin{displaymath}\dot x = A(t)x + A_1(t)x(t-h)+B(t)u\,.\end{displaymath}

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.

Received: June 15, 2010

AMS Subject Classification: 93D15, 93B05, 34K20

Key Words and Phrases: stabilization, time-varying, delay system, Riccati equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 1