Research Article Open Access

Stabilization of a Nonlinear Delay System

Walid Arouri1, Elyes Maherzi1, Mongi Besbes1 and Houda Ben Attia Sethom2
  • 1 ,
  • 2 , Afganistan
American Journal of Applied Sciences
Volume 9 No. 3, 2012, 405-416

DOI: https://doi.org/10.3844/ajassp.2012.405.416

Submitted On: 30 November 2011 Published On: 31 January 2012

How to Cite: Arouri, W., Maherzi, E., Besbes, M. & Sethom, H. B. A. (2012). Stabilization of a Nonlinear Delay System. American Journal of Applied Sciences, 9(3), 405-416. https://doi.org/10.3844/ajassp.2012.405.416

Abstract

Problem statement: The analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. This can affect their significantly operations. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. The delay may affect one or more states of the considered system. It may also affect the establishment of the command. Several studies have investigated the stability of delay systems under the assumption that the delay is a variable phenomenon; such variation is considered to be bounded or limited to facilitate analysis of the system. In this study we propose a modelling of delayed system by using the multimodels and switched system theory. The analysis of stability is based on the use of second Lyapunov method. The issued stability conditions are expressed as Bilinear Matrix Inequalities impossible to resolve. That’s why we propose the same original relaxations to come over this difficulty, an example of induction machine is given to illustrate over approach. Approach: We propose to use the control theory developed for switched systems to synthesis a control laws for the stabilisation of delays system. Results: We stabilize the induction machine around many operating points despite the non linearities. Conclusion: The developed method is less conservative and less pessimistic than the used classical methods.

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Keywords

  • Delay systems
  • lyapunov method
  • switching system
  • Linear Matrix Inequalities (LMI)
  • Bilinear Matrix Inequalities (BMI)