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http://dx.doi.org/10.5370/KIEE.2013.62.8.1144

Stabilizing Controller Design for Time-delay Singularly Perturbed Systems by H∞ Norm and Lambert W Function  

Kim, Beomsoo (Dept. of Mechanical System Engineering, Gyeongsang National University)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.62, no.8, 2013 , pp. 1144-1150 More about this Journal
Abstract
The stabilizing controller design problem of time-delay singularly perturbed systems is considered. The proposed approach is based on the $H_{\infty}$ norm and the composite control method. A sufficient condition for the stability of the time-delay slow subsystem is presented. Using this condition, we can construct the composite control law for the time-delay singularly perturbed system and analysis the system by the matrix Lambert W function. Illustrated examples are presented to demonstrate the validity and applicability of the proposed method.
Keywords
Time-delay singularly perturbed systems; $H_{\infty}$ norm; Lambert W function; Stabilizing control; Composite control;
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1 J. Richard, "Time-delay systems: An overview of some recent advances and open problems," Automatica, vol. 39, no. 10, pp. 1667-1694, 2003.   DOI   ScienceOn
2 Y. Kyrychko and S. Hogan, "On the use of delay equations in engineering applications," J. Vibrat. Control, vol. 16, no. 7-8, pp. 943-960, 2010.   DOI   ScienceOn
3 S. Yi, P. W. Nelson, and A. G. Ulsoy, Time-delay systems: Analysis and control using the Lambert W function, World Scientific Publishing Company, 2010.
4 P. Kokotovic, H. K. Khali, and J. O'Reilly, Singular perturbation methods in control: Analysis and design, Society for Industrial and Applied Mathematics, 1987.
5 K. W. Chang, "Singular perturbations of a general boundary value problem," SIAM Journal on Mathematical Analysis, vol. 3, no. 3, pp. 520-526, 1972.   DOI
6 Y. Kim, B. Kim, and M. Lim, "Finite-time composite control for a class of singularly perturbed nonlinear systems via successive Galerkin approximation," Control Theory and Applications, IEE Proceedings-, pp. 507-512, 2005.
7 N. Abdelkrim, A. Tellili, and M. N. Abdelkrim, "Composite control of a delayed singularly perturbed system by using Lambert-W function," Systems Signals and Devices (SSD), 2010 7th International Multi-Conference on, pp. 1-4, 2010.
8 S. Yi, P. Nelson, and A. Ulsoy, "Eigenvalue assignment via the Lambert W function for control of time-delay systems," J. Vibrat. Control, vol. 16, no. 7-8, pp. 961-982, 2010.   DOI   ScienceOn
9 S.T. Pan, C.F. Chen, and J.G. Hsieh, "Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays" , Journal of Dynamic Systems, Measurement, and Control, vol. 126, pp. 462-466, 2004   DOI   ScienceOn
10 Z. Shao and J. Rowland, "Stability of time-delay singularly perturbed systems," Control Theory and Applications, IEE Proceedings-, pp. 111-113, 1995.
11 C. Chen, "Stabilization for a class of two-time-scale multiple time-delay neutral systems," IEEE ICSS2005 International Conference On Systems & Signals, pp. 849-854, 2005.
12 N. Abdelkrim, A. Tellili, and M. N. Abdelkrim, "Additive fault tolerant control applied to delayed singularly perturbed system," Journal of Software Engineering and Applications, vol. 5, no. 4, pp. 217-224, 2012.   DOI
13 R. M. Corless, G. H. Gonnet, D. E. Hare, D. J. Jeffrey, and D. E. Knuth, "On the Lambert W function," Advances in Computational Mathematics, vol. 5, no. 1, pp. 329-359, 1996.   DOI   ScienceOn
14 H. Shinozaki and T. Mori, "Robust stability analysis of linear time-delay systems by Lambert W function," Proceedings of the Annual Conference of the Institute of Systems, Control and Information Engineers, pp. 389-390, 2005.
15 E. Jarlebring and T. Damm, "The Lambert W function and the spectrum of some multidimensional time-delay systems," Automatica, vol. 43, no. 12, pp. 2124-2128, 2007.   DOI   ScienceOn