Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 26, pp. 1-10.

Title: Linear uncertain non-autonomous time-delay systems:
       Stability and stabilizability  via Riccati equations
 
Authors: Piyapong Niamsup  (Chiangmai Univ., Thailand)
         Kanit Mukdasai (Institute of Math., Hanoi, Vietnam)
	 Vu N. Phat     (Institute of Math., Hanoi, Vietnam)

Abstract: 
 This paper addresses the problem of exponential stability for
 a class of uncertain linear non-autonomous time-delay
 systems. Here, the parameter uncertainties are
 time-varying and unknown but norm-bounded and the delays are
 time-varying.  Based on combination of the Riccati equation approach and
 the use of suitable Lyapunov-Krasovskii functional, new sufficient
 conditions for the robust stability   are obtained in terms
 of the solution of Riccati-type equations. The approach allows  to
 compute simultaneously the two bounds that characterize the
 exponential stability rate of the solution. As an application,
 sufficient conditions for the robust stabilization are  derived.
 Numerical examples illustrated the results are given.
 
Submitted September 28, 2007. Published February 22, 2008.
Math Subject Classifications: 93D15, 34D20, 49K20.
Key Words: Non-autonomous systems;  time-delay systems; uncertainties;
    exponential stability; stabilization; Lyapunov function; Riccati equation.