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IMA Journal of Mathematical Control and Information Advance Access originally published online on April 27, 2009
IMA Journal of Mathematical Control and Information 2009 26(2):163-177; doi:10.1093/imamci/dnp005
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Delay feedback control in exponential stabilization of linear time-varying systems with input delay

L. V. Hien{dagger}

Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Road, Hanoi, Vietnam

V. N. Phat

Institute of Mathematics, 18 Hoang Quoc Viet Road, Hanoi, Vietnam

{dagger} Email: hienlv{at}hnue.edu.vn

Received on February 20, 2008; Revision received March 1, 2009. Accepted on March 18, 2009

In this paper, we investigate the memory controller design for the exponential stabilization of linear time-varying systems with control delay. Based on state transformation and an improved Lyapunov–Krasovskii functional, new sufficient conditions for the exponential stabilization of the system are derived to design memory feedback controller which makes the system exponentially stabilizable. The conditions are given in terms of the solution of appropriate Riccati differential equations, which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. An application to robust control of uncertain linear control systems with input delay as well as illustrative examples to show the effectiveness of the obtained results is given.

Keywords: exponential stability; Riccati equation; input delay; time-varying systems.


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