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		Shuai LIU,Lihua XIE,Huanshui ZHANG.[en_title][J].Control Theory and Technology,2010,8(3):368~374.[Copy]

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ShuaiLIU,LihuaXIE,HuanshuiZHANG
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DOI：10.1007/s11768-010-0039-2

Received:February 04, 2010Revised:February 04, 2010

基金项目:This work was supported by the National Natural Science Foundation of China (No.60828006), the National Natural Science Foundation for Distinguished Young Scholars of China (No.60825304), and the Major State Basic Research Development Program of China (973 Program) (No.2009cb320600).

Infinite horizon LQR for systems with multiple delays in a single input channel

Shuai LIU,Lihua XIE,Huanshui ZHANG

(Nanyang Technological University;School of EEE, Nanyang Technological University, Singapore;Shandong University)

Abstract:

This paper is concerned with the linear quadratic regulation (LQR) problem for both linear discrete-time systems and linear continuous-time systems with multiple delays in a single input channel. Our solution is given in terms of the solution to a two-dimensional Riccati difference equation for the discrete-time case and a Riccati partial differential equation for the continuous-time case. The conditions for convergence and stability are provided.

Key words: Input delay systems Linear quadratic regulation Riccati difference and differential equations Stability analysis