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Iterative LMI approach to design robust state-feedback controllers for Lur’e systems with time-invariant delays

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  • Control Theory
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Abstract

In this paper, we present a design of robust state-feedback stabilization and a design of robust state-feedback H ∞ control for Lur’e systems with time-invariant delays and norm-bounded uncertainties. The criteria of state-feedback stabilization and state-feedback H ∞ control are developed using Lyapunov-Krasovskii Theorem with a delay-partitioning Lyapunov-Krasovskii functional and an integral of sector-bounded nonlinearities. The design criteria are given in terms of bilinear matrix inequality, which is non-convex optimization. We develop algorithms based on coordinate optimization, which alternate between two LMI optimization problems, to solve for the robust state-feedback controllers. The proposed iterative LMI algorithm for H ∞ control design is a local optimization procedure, but it can return satisfactory state-feedback controllers depending on the initialization. Numerical examples show that the proposed LMI algorithms can provide robust state-feedback stabilization to guarantee the closed-loop stability of LSTD and yield robust state-feedback control to guarantee the worstcase H ∞ performance of the closed-loop LSTD.

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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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Corresponding author

Correspondence to David Banjerdpongchai.

Additional information

Recommended by Editor Ju Hyun Park.

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. and Ph.D. degrees in Electrical Engineering from Chulalongkorn University, in 2002 and 2014, respectively. 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. Iterative LMI approach to design robust state-feedback controllers for Lur’e systems with time-invariant delays. Int. J. Control Autom. Syst. 13, 1086–1096 (2015). https://doi.org/10.1007/s12555-014-0103-7

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  • DOI: https://doi.org/10.1007/s12555-014-0103-7

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