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IMA Journal of Mathematical Control and Information 2004 21(3):261-273; doi:10.1093/imamci/21.3.261
© 2004 by Institute of Mathematics and its Applications
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An LMI approach to positive real control for discrete time-delay systems

Shengyuan Xu1, Junwei Lu2, Shaosheng Zhou3 and Chengwu Yang4

1 Department of Automation, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China 2 College of Electrical and Electronic Engineering, Nanjing Normal University, 78 Bancang Street, Nanjing, 210042, People's Republic of China 3 Institute of Automation, Qufu Normal University, Qufu 273165, Shandong, People's Republic of China 4 810 Division, School of Power Engineering, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China

This paper focuses on the problem of positive real control for discrete time-delay systems. The problem we address is the design of a dynamic output feedback controller, which guarantees the asymptotic stability of the closed-loop system and achieves the extended strictly positive realness of a certain closed-loop transfer function. Then, a condition for extended strictly positive realness for discrete-delay systems is developed. Based on this, a sufficient condition for the existence of the desired controllers is proposed in terms of three linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit parametrization of the desired output feedback controller is presented. An illustrative example is given to demonstrate the applicability of the proposed approach.

Keywords: discrete-delay systems; positive real control; output feedback; linear matrix inequality (LMI).

Received 14 March 2002.


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