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Guaranteed cost control of linear systems with distributed delays: A complete type functionals approach

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  • Control Theory
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Abstract

The design of a control law guaranteeing an upper bound on the performance index of linear systems with point wise and distributed delay is addressed. The control law is computed through an iterative procedure: at each step, it is the solution that minimizes the Bellman type equation obtained from plugging in the functional of complete type associated to the closed loop system of the previous step. It is shown that at each step, the closed loop system remains into the class of systems with distributed delays, the stability of the closed loop is maintained, and the guaranteed cost does not increase. The allowed continuous time varying norm bounded uncertainties guaranteeing the cost are also characterized. An illustrative example validates the approach.

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Authors and Affiliations

  1. CITIS-ICBI, Universidad Autónoma del Estado de Hidalgo, Carretera Pachuca — Tulancingo, Km. 4.5, C. U. Pachuca, Hidalgo, México

    Omar Santos

  2. Department of Automatic Control, CINVESTAV-IPN, A. P. 14-740, México, D. F., México

    Sabine Mondié

Authors
  1. Omar Santos
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  2. Sabine Mondié
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Correspondence to Omar Santos.

Additional information

Recommended by Editorial Board member Myotaeg Lim under the direction of Editor Young Il Lee. This work was supported by Supported by Conacyt Project 61076.

Omar Santos received his B.S. degree from Minatitlan Institute of Technology, Minatitlan, Veracruz, Mexico, an M.S. degree in Electrical Engineering with option on Automatic Control in 2000 and a Ph.D. in 2006 from the Department of Automatic Control, CINVESTAV-IPN, Mexico. From 2001 to the present, he is with the State Autonomous University of Hidalgo, Pachuca, Hidalgo, Mexico. His research interests include time delay systems and nonlinear control.

Sabine Mondié received her B.S. degree in Industrial Engineering from the ITESM, Mexico City, and her M.S. and Ph.D. degrees in Electrical Engineering from the CINVESTAV, Mexico City and the IRCyN, Nantes, France, in 1983 and 1996, respectively. Since 1996, she is a Professor at the Department of Automatic Control at CINVESTAV, Mexico City, Mexico. Her research interests include time delay systems, the structural approach of linear systems, and their applications.

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Santos, O., Mondié, S. Guaranteed cost control of linear systems with distributed delays: A complete type functionals approach. Int. J. Control Autom. Syst. 8, 497–505 (2010). https://doi.org/10.1007/s12555-010-0302-9

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  • DOI: https://doi.org/10.1007/s12555-010-0302-9

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