Finite‐timeH ∞ control for discrete‐time switched nonlinear systems with time delay

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Abstract
Summary: In this paper, the problem of finite‐timeH ∞ control is addressed for a class of discrete‐time switched nonlinear systems with time delay. The concept ofH ∞ 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 theH ∞ finite‐time boundedness of the closed‐loop system. Then, a finite‐timeH ∞ state feedback controller is also designed by solving such conditions. Furthermore, the problem of uniform finite‐timeH ∞ 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.
Funding Information
  • National Natural Science Foundation of China (61273123)
  • Australian Research Council
  • Program for New Century Excellent Talents in University (NCET-13-0878)

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