Geodesic
Linear uncertain non-autonomous time-delay systems: Stability and stabilizability via Riccati equations
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 93D15, 34D20, 49K20
Keywords: non-autonomous systems, time-delay systems, uncertainties, exponential stability, stabilization, Lyapunov function, Riccati equation 
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     author = {Niamsup, Piyapong and Mukdasai, Kanit and Phat, Vu N.},
     title = {Linear uncertain non-autonomous time-delay systems: {Stability} and stabilizability via {Riccati} equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
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Niamsup, Piyapong; Mukdasai, Kanit; Phat, Vu N. Linear uncertain non-autonomous time-delay systems: Stability and stabilizability via Riccati equations. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a50/