IJPAM: Volume 63, No. 4 (2010)

STABILITY OF LINEAR TIME-VARYING SYSTEMS

Kreangkri Ratchagit
Deparment of Mathematics
Faculty of Science
Maejo University
Chiang Mai, 50290, THAILAND
e-mail: [email protected]


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 be constructed and verifyed. We provide a step-by-step procedure for finding feedback controllers.

Received: March 27, 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: 63
Issue: 4