Electron. J. Diff. Eqns., Vol. 2008(2008), No. 26, pp. 1-10.

Linear uncertain non-autonomous time-delay systems: Stability and stabilizability via Riccati equations

Piyapong Niamsup, Kanit Mukdasai, Vu N. Phat

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.

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Piyapong Niamsup
Department of Mathematics, Chiangmai University
Chiangmai 50200, Thailand
email: scipnmsp@chiangmai.ac.th
Kanit Mukdasai
Department of Mathematics, Chiangmai University
Chiangmai 50200, Thailand
email: kanitmukdasai@hotmail.com
Vu Ngoc Phat
Institute of Mathematics
18 Hoang Quoc Viet Road, Hanoi, Vietnam
email: vnphat@math.ac.vn

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