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Nonfragile guaranteed cost control for Delta operator-formulated uncertain time-delay systems

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Abstract

With consideration that the controller parameters may vary from the designed value when the controller is realized, based on Lyapunov stability theory, a design method of nonfragile guaranteed cost control for a class of Delta operator-formulated uncertain time-delay systems is studied. A sufficient condition for the existence of the nonfragile guaranteed cost controller is given. A numeric example is then given to illustrate the effectiveness and the feasibility of the designed method. The results show that even if the parameters of the designed controller are of variations, the closed-loop system is still asymptotically stable and the super value of the cost function can also be obtained, while the closed-loop system will be unstable if the variations of the controller parameters are not considered when the controller is designed. The nonfragile guaranteed cost controller derived from the traditional shift operator method may cause the closed-loop system to be unstable, while the nonfragile guaranteed cost controller based on Delta operator method can avoid the unstable problem of the closed-loop system.

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Authors and Affiliations

  1. College of Electrical Engineering and Automation, Fuzhou University, Fuzhou Fujian, 350108, China

    Ruiquan Lin, Silian Chen & Xuwei Ding

Authors
  1. Ruiquan Lin
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  2. Silian Chen
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  3. Xuwei Ding
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Additional information

This work was supported by the Natural Science Foundation of Fujian Province (No.2008J04016).

Ruiquan LIN was born in 1971, Ph.D. He is an associate professor in the College of the Electrical Engineering and Automation of Fuzhou University. His research interests include Delta operator theory and nonfragile control.

Silian CHEN was born in 1984. She is a postgraduate in the College of the Electrical Engineering and Automation of Fuzhou University. Her research interests include Delta operator theory and nonfragile control. Xuwei DING was born in 1987. He is a postgraduate in the College of the Electrical Engineering and Automation of Fuzhou University. His research interests include Delta operator theory and nonfragile control.

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Lin, R., Chen, S. & Ding, X. Nonfragile guaranteed cost control for Delta operator-formulated uncertain time-delay systems. J. Control Theory Appl. 8, 233–238 (2010). https://doi.org/10.1007/s11768-010-8082-6

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  • DOI: https://doi.org/10.1007/s11768-010-8082-6

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