Technical Briefs

Memoryless Adaptive Controller Design for Uncertain Polynomial Systems With Multiple Time Delays

[+] Author and Article Information
Chang-Chun Hua

Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China; Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, Chinacch@ysu.edu.cn

Qing-Guo Wang

Department of Electrical and Computer Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore

Peng Shi

Faculty of Advanced Technology, University of Glamorgan, Pontypridd, Wales CF371DL, UK; Faculty of Health, Engineering and Science, Victoria University, Melbourne, Victoria 8001, Australia

Xin-Ping Guan

Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China; Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China

J. Dyn. Sys., Meas., Control 130(4), 044504 (Jun 09, 2008) (7 pages) doi:10.1115/1.2936867 History: Received March 20, 2007; Revised February 29, 2008; Published June 09, 2008

The stabilization problem is investigated for a class of uncertain systems with multiple time-varying delays. The considered system includes the uncertain nonlinear time delay functions, whose bounds are in the form of polynomial-type functions with unknown coefficients. The system is decomposed into two subsystems based on the input matrix. For the first subsystem, a time delay dependent linear virtual control input is constructed. Then, a memoryless state feedback controller is designed based on backstepping method. By employing new Lyapunov–Krasovskii functional, we show that the closed-loop system is exponentially stable. Finally, simulations are conducted to verify the effectiveness of the proposed method.

Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

The state response

Grahic Jump Location
Figure 2

Adaptive parameter and control input



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