Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 26, pp. 110.
Linear uncertain nonautonomous timedelay systems:
Stability and stabilizability via Riccati equations
Piyapong Niamsup, Kanit Mukdasai, Vu N. Phat
Abstract:
This paper addresses the problem of exponential stability for
a class of uncertain linear nonautonomous timedelay
systems. Here, the parameter uncertainties are
timevarying and unknown but normbounded and the delays are
timevarying. Based on combination of the Riccati equation approach and
the use of suitable LyapunovKrasovskii functional, new sufficient
conditions for the robust stability are obtained in terms
of the solution of Riccatitype 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: Nonautonomous systems; timedelay 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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