Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control |
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Authors: | Hui Lv Qingling Zhang Xinggang Yan |
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Affiliation: | 1. Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110819, China;2. Key Laboratory of Integrated Automation of Process Industry, Ministry of Education, Northeastern University, Shenyang, Liaoning 110819, China;3. Instrumentation, Control and Embedded Systems Research Group, School of Engineering & Digital Arts, University of Kent, Canterbury, Kent CT2 7NT, United Kingdom |
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Abstract: | This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional‐derivative control strategy is presented, where the derivative gain is to make the closed‐loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | robust normalization guaranteed cost control uncertain singular Markovian jump systems proportional‐derivative control impulsive control |
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