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On computing maximum allowable time delay of Lur’e systems with uncertain time-invariant delays

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  • Control Theory
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Abstract

In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix eliminating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.

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Authors and Affiliations

  1. Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, 254 Phayathai Road, Pathumwan, Bangkok, 10330, Thailand

    Thapana Nampradit & David Banjerdpongchai

Authors
  1. Thapana Nampradit
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  2. David Banjerdpongchai
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Correspondence to David Banjerdpongchai.

Additional information

Recommended by Associate Editor Soohee Han under the direction of Editor Hyungbo Shim.

This work was supported by Thailand Research Fund through the Royal Golden Jubilee Ph.D. Program under Grant No. PHD/0148/2003.

Thapana Nampradit received his B.Eng. degree in Control Engineering from King Mongkut’s Institute of Technology Ladkrabang in 1998, and his M.Eng. degree in Electrical Engineering from Chulalongkorn University in 2002. He is currently a Ph.D. candidate at the Department of Electrical Engineering, Chulalongkorn University. His research interests include robust control, numerical optimization, and computer-aided control systems design.

David Banjerdpongchai received his B.Eng. degree (First class honors) from Chulalongkorn University, and his M.S. and Ph.D. degrees from Stanford University, all in Electrical Engineering, in 1990, 1993, and 1997, respectively. Since 1990, he has been with the department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University. Currently, he is a professor of Electrical Engineering and head of department. He is a senior member of IEEE and has served as a chair of automatic control of ECTI Association since 2010. His research interests are energy management systems, analysis and synthesis of robust control systems, and convex optimization in robust control problems.

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Nampradit, T., Banjerdpongchai, D. On computing maximum allowable time delay of Lur’e systems with uncertain time-invariant delays. Int. J. Control Autom. Syst. 12, 497–506 (2014). https://doi.org/10.1007/s12555-013-0433-x

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  • DOI: https://doi.org/10.1007/s12555-013-0433-x

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