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Shock and Vibration
Volume 20 (2013), Issue 2, Pages 227-246

Experimental Study of H Control of Flexible Plate with Time Delay

Tong Zhao, Long-Xiang Chen, and Guo-Ping Cai

Department of Engineering Mechanics, State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai, China

Received 13 February 2012; Revised 14 May 2012

Copyright © 2013 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents theoretical and experimental studies of H control of a flexible plate with time delay. A matrix inequality used for stability analysis is proposed and proved by using the Lyapunov-Krasovskii functional and free-weighting matrix. An H controller is designed based on the matrix inequality and by using the parameter-adjusting method. Three control scenarios are discussed in detail by transforming the problem into parameters optimization: (i) controller design when maximum time delay of the system is known; (ii) allowable time delay when controller is known; (iii) the biggest allowable time delay to guarantee system stability when controller is unknown. Numerical simulations and experiments are also given to demonstrate the validity and feasibility of the proposed methods in this paper.