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Mathematical Problems in Engineering
Volume 2015, Article ID 125343, 10 pages
Research Article

Robust Stabilization and Disturbance Rejection of Positive Systems with Time-Varying Delays and Actuator Saturation

1School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
2School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China

Received 11 June 2014; Accepted 17 August 2014

Academic Editor: Mohammed Chadli

Copyright © 2015 Xi Ding et al. 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 focuses on the problems of robust stabilization and disturbance rejection for a class of positive systems with time-varying delays and actuator saturation. First, a convex hull representation is used to describe the saturation characteristics. By constructing an appropriate copositive type Lyapunov functional, we give sufficient conditions for the existence of a state feedback controller such that the closed-loop system is positive and asymptotically stable at the origin of the state space with a domain of attraction. Then, the disturbance rejection performance analysis in the presence of actuator saturation is developed via -gain. The design method is also extended to investigate the problem of -gain analysis for uncertain positive systems with time-varying delays and actuator saturation. Finally, three examples are provided to demonstrate the effectiveness of the proposed method.