# American Institute of Mathematical Sciences

2015, 5(1): 11-23. doi: 10.3934/naco.2015.5.11

## Delay-range dependent $H_\infty$ control for uncertain 2D-delayed systems

 1 College of Sciences, Liaoning Shihua University, Fushun, Liaoning 113001, China, China 2 Department of Chemical & Biochemical Engineering, College of Chemistry & Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China 3 Department of Chemical and Biomolecular Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

Received  December 2014 Revised  March 2015 Published  March 2015

This paper proposes a delay-range dependent method to solve a two-dimensional (2D) stabilization and $H_\infty$ control problem for a class of uncertain delayed systems described by the Roessor model with a range delay. By using a new 2D Lyapunov-Krasovskii function and introducing a differential inequality to the difference Lyapunov functional for 2D systems, sufficient delay-range dependent conditions for the existence of the proposed feedback controller scheme are established in terms of linear matrix inequalities (LMIs), which depend on both the difference between the upper and lower delay bounds and the upper delay bound of the interval time-varying delay. By solving these LMIs, the 2D law is explicitly formulated, together with an adjustable robust $H_\infty$ performance level. The analysis of the application in the thermal process demonstrates the effectiveness of the proposed controller.
Citation: Li-Min Wang, Jing-Xian Yu, Jia Shi, Fu-Rong Gao. Delay-range dependent $H_\infty$ control for uncertain 2D-delayed systems. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 11-23. doi: 10.3934/naco.2015.5.11
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