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Practical stability and stabilization of a class of nonlinear neutral type time delay systems with multiple delays: BMI’s approaches

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Abstract

In this paper, the practical stability and stabilization of a class of nonlinear neutral type time delay systems with multiple delays and bounded perturbations is discussed. Sufficient conditions based on Lyapunov-Krasovskii functionals are derived. They are formulated in terms of the feasibility of a set of Bilinear Matrix Inequalities (BMI’s). A practical exponential estimate of the system response is also obtained. This approach is shown to be useful in the solution of an engineering problem: the elimination of the stick-slip phenomenon in the drilling process.

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Authors and Affiliations

  1. Research Center on Information Technology and Systems, Hidalgo State University, Pachuca-Hidalgo C.P., 42084, México

    Raúl Villafuerte

  2. Automatic Control Department of CINVESTAV-IPN D.F, Pachuca-Hidalgo C.P., A.P. 07300, México

    Belem Saldivar & Sabine Mondié

Authors
  1. Raúl Villafuerte
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  2. Belem Saldivar
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  3. Sabine Mondié
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Corresponding author

Correspondence to Raúl Villafuerte.

Additional information

Recommended by Editor Ju Hyun Park.

This research is supported by CONACyT, Grant 180725 and by PROMEP-NPTC.

Raúl Vilafuerte received his B.S. degree in Physics and Mathematics engineering from ESFM-IPN, Mexico City, Mexico in 2004, and his M.S. and Ph.D. degrees in Automatic Control from CINVESTAV-IPN, Mexico City, México in 2006 and 2010, respectively. Since 2011, he has been a Professor at the CITIS-UAEH, Hidalgo, Mexico. His research interests include time delay systems and nonlinear control.

Belem Saldivar received her B.S. degree in Electronics and Telecommunications Engineering from UAEH, Pachuca Hidalgo, Mexico, in 2007. She obtained her M.S. degree in Automatic Control from CINVESTAV, Mexico City, Mexico in 2010. In April 2013, she presented her dissertation defense to obtain her Ph.D. degree in Automatic Control from CINVESTAV, Mexico City, Mexico and the Ph.D. degree in informatics and applications from IRCCyN, Nantes, France. Her research is focused on the modeling analysis and control of oil well drilling systems based on neutral functional differential equation and partial differential equation models.

Sabine Mondié received her B.S. degree in Industrial Engineering from the ITESM, Mexico City, Mexico, in 1981, and her M.S. and Ph.D. degrees in Electrical Engineering from CINVESTAV, Mexico City, Mexico and IRCCyN, Nantes, France, in 1983 and 1996, respectively. Since 1996, she has been a Professor at the Department of Automatic Control of CINVESTAV, Mexico City, Mexico. Her research is focused on time delay systems, their analysis, control and applications.

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Villafuerte, R., Saldivar, B. & Mondié, S. Practical stability and stabilization of a class of nonlinear neutral type time delay systems with multiple delays: BMI’s approaches. Int. J. Control Autom. Syst. 11, 859–867 (2013). https://doi.org/10.1007/s12555-013-0083-z

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