- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 595029, 10 pages
On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties
1Department of Academic Areas of Jataí, Federal Institute of Education, Science and Technology of Goiás (IFG), Campus Jataí, 75804-020 Jataí, GO, Brazil
2Department of Electrical Engineering, UNESP, Univ Estadual Paulista, Campus de Ilha Solteira, 15385-000 Ilha Solteira, SP, Brazil
3Department of Computer, Telecommunication, Control, and Automation Engineering, Faculdade of Science and Technology of Montes Claros (FACIT), Campus II, 39400-141 Montes Claros, MG, Brazil
Received 17 January 2013; Accepted 12 April 2013
Academic Editor: Oleg V. Gendelman
Copyright © 2013 Wallysonn A. de Souza et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. A. Wicks, P. Peleties, and R. A. DeCarlo, “Construction of piecewise Lyapunov functions for stabilizing switched systems,” in Proceedings of the 33rd IEEE Conference on Decision and Control, vol. 4, pp. 3492–3497, December 1994.
- D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, no. 5, pp. 59–70, 1999.
- R. A. Decarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, “Perspectives and results on the stability and stabilizability of hybrid systems,” Proceedings of the IEEE, vol. 88, no. 7, pp. 1069–1082, 2000.
- J. P. Hespanha and A. S. Morse, “Switching between stabilizing controllers,” Automatica, vol. 38, no. 11, pp. 1905–1917, 2002.
- Z. Sun and S. S. Ge, “Analysis and synthesis of switched linear control systems,” Automatica, vol. 41, no. 2, pp. 181–195, 2005.
- A. Feuer, G. C. Goodwin, and M. Salgado, “Potential benefits of hybrid control for linear time invariant plants,” in Proceedings of the American Control Conference (ACC '97), vol. 5, pp. 2790–2794, June 1997.
- N. H. Mcclamroch and I. Kolmanovsky, “Performance benefits of hybrid control design for linear and nonlinear systems,” Proceedings of the IEEE, vol. 88, no. 7, pp. 1083–1096, 2000.
- H. Ishii and B. A. Francis, “Stabilizing a linear system by switching control with dwell time,” IEEE Transactions on Automatic Control, vol. 47, no. 12, pp. 1962–1973, 2002.
- D. J. Leith, R. N. Shorten, W. E. Leithead, O. Mason, and P. Curran, “Issues in the design of switched linear control systems: a benchmark study,” International Journal of Adaptive Control and Signal Processing, vol. 17, no. 2, pp. 103–118, 2003.
- S. Pettersson, “Controller design of switched linear systems,” in Proceedings of the American Control Conference (AAC '04), vol. 4, pp. 3869–3874, Boston, Mass, USA, July 2004.
- H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308–322, 2009.
- J. C. Geromel and G. S. Deaecto, “Switched state feedback control for continuous-time uncertain systems,” Automatica, vol. 45, no. 2, pp. 593–597, 2009.
- N. Otsuka and T. Soga, “Quadratic stabilizability for polytopic uncertain continuoustime switched linear systems composed of two subsystems,” International Journal of Control and Automation, vol. 3, no. 1, pp. 35–42, 2010.
- G. S. Deaecto, J. C. Geromel, and J. Daafouz, “Switched state-feedback control for continuous time-varying polytopic systems,” International Journal of Control, vol. 84, no. 9, pp. 1500–1508, 2011.
- D. Xie and M. Yu, “Stability analysis of switched linear systems with polytopic uncertainties,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics (SMC '06), vol. 5, pp. 3749–3753, October 2006.
- G. Zhai, H. Lin, and P. J. Antsaklis, “Quadratic stabilizability of switched linear systems with polytopic uncertainties,” International Journal of Control, vol. 76, no. 7, pp. 747–753, 2003.
- S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1994.
- J. Löfberg, “YALMIP: a toolbox for modeling and optimization in MATLAB,” in Proceedings of the 2004 IEEE International Symposium on Computer Aided Control System Design, pp. 284–289, September 2004.
- J. F. Sturm, “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,” Optimization Methods and Software, vol. 11-12, no. 1, pp. 625–653, 1999.
- J. Bernussou, P. L. D. Peres, and J. C. Geromel, “A linear programming oriented procedure for quadratic stabilization of uncertain systems,” Systems and Control Letters, vol. 13, no. 1, pp. 65–72, 1989.
- D. D. Šiljak and D. M. Stipanović, “Robust stabilization of nonlinear systems: the LMI approach,” Mathematical Problems in Engineering, vol. 6, no. 5, pp. 461–493, 2000.
- R. Cardim, M. C. M. Teixeira, E. Assuncao et al., “Implementation of a DC-DC converter with variable structure control of switched systems,” in Proceedings of the IEEE International Electric Machines Drives Conference (IEMDC '11), pp. 872–877, Niagara Falls, Canada, May 2011.
- R. Cardim, M. C. M. Teixeira, E. Assunção, et al., “Design and implementation of a DC-DC converter based on variable structure control of switched systems,” in 18th IFAC World Congress, vol. 18, pp. 11048–11054, Milan, Italy, 2011.
- B. R. Barmish, “Stabilization of uncertain systems via linear control,” IEEE Transactions on Automatic Control, vol. 28, no. 8, pp. 848–850, 1983.
- M. J. Corless and G. Leitmann, “Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems,” IEEE Transactions on Automatic Control, vol. 26, no. 5, pp. 1139–1144, 1981.
- M. P. A. Santim, M. C. M. Teixeira, W. A. de Souza, R. Cardim, and E. Assunção, “Design of a Takagi-Sugeno fuzzy regulator for a set of operation points,” Mathematical Problems in Engineering, vol. 2012, Article ID 731298, 17 pages, 2012.
- R. Cardim, M. C. M. Teixeira, E. Assunção, and M. R. Covacic, “Variable-structure control design of switched systems with an application to a DC-DC power converter,” IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3505–3513, 2009.