Finite‐time H ∞ control for discrete‐time switched nonlinear systems with time delay |
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Authors: | Guangdeng Zong Ruihua Wang Weixing Zheng Linlin Hou |
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Affiliation: | 1. Institute of Automation, Qufu Normal University, Qufu, Shandong, China;2. School of Computing, Engineering and Mathematics, University of Western Sydney, Penrith, Australia |
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Abstract: | In this paper, the problem of finite‐time H ∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept of H ∞ finite‐time boundedness is first introduced for discrete‐time switched delay systems. Next, a set of switching signals are designed by using the average dwell time approach, under which some delay‐dependent sufficient conditions are derived to guarantee the H ∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐time H ∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐time H ∞ stabilization is also resolved. All the conditions are cast into linear matrix inequalities, which can be easily checked by using recently developed algorithms for solving linear matrix inequalities. A numerical example and a water‐quality control system are provided to demonstrate the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | Switched delay systems finite‐time boundedness H ∞ control delay‐dependent stability conditions average dwell time |
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