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H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers

Year 2015, Volume: 3 Issue: 2, 102 - 107, 30.03.2015
https://doi.org/10.18100/ijamec.47841

Abstract

The paper deals with the problem of the H control of continuous-time linear systems by proper dynamic output controllers of order equal to the plant model order and by static output controller. The design procedure is based on solution of the set of linear matrix inequalities and the matrix equality and ensures the closed-loop asymptotic stability using Lyapunov approach and the Hperformance, to guarantee the closed-loop system robustness to unknown disturbance. Numerical examples are given to illustrate the design procedures and the relevance of the method as well as to validate the performances of the proposed approach.

References

  • Chadli, M., Maquin, D. and Ragot, J. Static output feedback for Takagi-Sugeno systems: An LMI approach, Proceedings of the 10th Mediterranean Conference on Control and Automation (MED2002), 9-13 July 2002, Lisbon, Portugal.
  • Syrmos, V.L., Abdallah, C. and Dorato, P. Static output feedback: A survey, Proceedings of the 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, USA, 14-16 December 1994, pp. 837-842.
  • Syrmos, V.L., Abdallah, C., Dorato, P. and Grigoriadis, K. Static output feedback: A survey, Automatica, Vol. 33, No. 2, 1997, pp. 125-137.
  • Krokavec, D. and Filasova, A. Design of fault residual functions for systems stabilized by static output feedback, Proceedings of the 2nd International Conference on Control and Fault-Tolerant Systems (SysTol'13), Nice, France, Oct 9-11 October 2013, pp. 596-600.
  • Astolfi, A. and Colaneri, P. The static output feedback stabilization problem as a concave-convex programming problem, Proceedings 2004 American Control Conference, Boston, MA, USA, 30 June – 2 July 2004, pp. 2139-2141.
  • Lewis, F.L. and Syrmos, V.L. Optimal Control, John Wiley & Sons, New York, NY, USA, 1995.
  • Crusius, C.A.R. and Trofino, A. Sufficient LMI conditions for output feedback control problems, IEEE Transactions on. Automatic Control, Vol. 44, No. 5, 1999, pp. 1053-1057.
  • Jungers, M., Castelan, E.B., Moraes, V.M. and Moreno, U.F. A dynamic output feedback controller for NCS based on delay estimates, Automatica, Vol. 49, No. 3, 2013, pp. 788-792.
  • El Ghaoui, L. and Balakrishnan, V. Synthesis of fixed-structure controllers via numerical optimization, Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, USA, 14-16 December 1994, pp. 2678-2683.
  • de Oliveira, M.C., Camino, J.E. and Skelton, R.E. A convexifying algorithm for the design of structured linear controllers, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 12-15 December 2000, pp. 2781-2786.
  • Scherer, C., Gahinet, P. and Chilali, M. Multiobjective output-feedback control via LMI optimization, IEEE Transactions on Automatic Control, Vol. 42, No. 7, 1997, pp. 896-911.
  • Filasova, A. and Krokavec, D. Pairwise control principle in large-scale systems, Archives of Control Sciences, Vol. 21, No. 3, 2011, pp. 227-242.
  • Wang, Q.G. Decoupling Control. Springer-Verlag Berlin, Germany, 2003.
  • Kailath, T. Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, USA, 1980.
  • Doyle, J.C., Glover, K., Khargonekar, P.P. and Francis, B.A. State-space solutions to standard H2 and H∞ control problems, IEEE Transactions on Automatic Control, Vol. 34, No. 8, 1989, pp. 831-847.
  • Krokavec, D., Filasova, A. and Liscinsky, P. Dynamic output control of nonlinear systems described by Takagi-Sugeno models. Proceedings of the 2014 IEEE Multi-conference on Systems and Control (MSC 2014), Part: 2014 IEEE International Conference on Control Applications (CCA 2014), 8-10 October 2014, Antibes, France, pp. 959-964.
  • Kautsky, J., Nichols, N.K. and Van Dooren, P. Robust pole assignment in linear state feedback, International Journal of Control, Vol. 41, No.5, 1985, pp. 1129-1155.
  • Peaucelle, D., Henrion, D., Labit, Y. and Taitz, K. User's Guide for SeDuMi Interface 1.04, LAAS-CNRS, Toulouse, France, 2002.

Original Research Paper

Year 2015, Volume: 3 Issue: 2, 102 - 107, 30.03.2015
https://doi.org/10.18100/ijamec.47841

Abstract

References

  • Chadli, M., Maquin, D. and Ragot, J. Static output feedback for Takagi-Sugeno systems: An LMI approach, Proceedings of the 10th Mediterranean Conference on Control and Automation (MED2002), 9-13 July 2002, Lisbon, Portugal.
  • Syrmos, V.L., Abdallah, C. and Dorato, P. Static output feedback: A survey, Proceedings of the 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, USA, 14-16 December 1994, pp. 837-842.
  • Syrmos, V.L., Abdallah, C., Dorato, P. and Grigoriadis, K. Static output feedback: A survey, Automatica, Vol. 33, No. 2, 1997, pp. 125-137.
  • Krokavec, D. and Filasova, A. Design of fault residual functions for systems stabilized by static output feedback, Proceedings of the 2nd International Conference on Control and Fault-Tolerant Systems (SysTol'13), Nice, France, Oct 9-11 October 2013, pp. 596-600.
  • Astolfi, A. and Colaneri, P. The static output feedback stabilization problem as a concave-convex programming problem, Proceedings 2004 American Control Conference, Boston, MA, USA, 30 June – 2 July 2004, pp. 2139-2141.
  • Lewis, F.L. and Syrmos, V.L. Optimal Control, John Wiley & Sons, New York, NY, USA, 1995.
  • Crusius, C.A.R. and Trofino, A. Sufficient LMI conditions for output feedback control problems, IEEE Transactions on. Automatic Control, Vol. 44, No. 5, 1999, pp. 1053-1057.
  • Jungers, M., Castelan, E.B., Moraes, V.M. and Moreno, U.F. A dynamic output feedback controller for NCS based on delay estimates, Automatica, Vol. 49, No. 3, 2013, pp. 788-792.
  • El Ghaoui, L. and Balakrishnan, V. Synthesis of fixed-structure controllers via numerical optimization, Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, USA, 14-16 December 1994, pp. 2678-2683.
  • de Oliveira, M.C., Camino, J.E. and Skelton, R.E. A convexifying algorithm for the design of structured linear controllers, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 12-15 December 2000, pp. 2781-2786.
  • Scherer, C., Gahinet, P. and Chilali, M. Multiobjective output-feedback control via LMI optimization, IEEE Transactions on Automatic Control, Vol. 42, No. 7, 1997, pp. 896-911.
  • Filasova, A. and Krokavec, D. Pairwise control principle in large-scale systems, Archives of Control Sciences, Vol. 21, No. 3, 2011, pp. 227-242.
  • Wang, Q.G. Decoupling Control. Springer-Verlag Berlin, Germany, 2003.
  • Kailath, T. Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, USA, 1980.
  • Doyle, J.C., Glover, K., Khargonekar, P.P. and Francis, B.A. State-space solutions to standard H2 and H∞ control problems, IEEE Transactions on Automatic Control, Vol. 34, No. 8, 1989, pp. 831-847.
  • Krokavec, D., Filasova, A. and Liscinsky, P. Dynamic output control of nonlinear systems described by Takagi-Sugeno models. Proceedings of the 2014 IEEE Multi-conference on Systems and Control (MSC 2014), Part: 2014 IEEE International Conference on Control Applications (CCA 2014), 8-10 October 2014, Antibes, France, pp. 959-964.
  • Kautsky, J., Nichols, N.K. and Van Dooren, P. Robust pole assignment in linear state feedback, International Journal of Control, Vol. 41, No.5, 1985, pp. 1129-1155.
  • Peaucelle, D., Henrion, D., Labit, Y. and Taitz, K. User's Guide for SeDuMi Interface 1.04, LAAS-CNRS, Toulouse, France, 2002.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Dusan Krokavec

Anna Filasova This is me

Publication Date March 30, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Krokavec, D., & Filasova, A. (2015). H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers. International Journal of Applied Mathematics Electronics and Computers, 3(2), 102-107. https://doi.org/10.18100/ijamec.47841
AMA Krokavec D, Filasova A. H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers. International Journal of Applied Mathematics Electronics and Computers. March 2015;3(2):102-107. doi:10.18100/ijamec.47841
Chicago Krokavec, Dusan, and Anna Filasova. “H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers”. International Journal of Applied Mathematics Electronics and Computers 3, no. 2 (March 2015): 102-7. https://doi.org/10.18100/ijamec.47841.
EndNote Krokavec D, Filasova A (March 1, 2015) H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers. International Journal of Applied Mathematics Electronics and Computers 3 2 102–107.
IEEE D. Krokavec and A. Filasova, “H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers”, International Journal of Applied Mathematics Electronics and Computers, vol. 3, no. 2, pp. 102–107, 2015, doi: 10.18100/ijamec.47841.
ISNAD Krokavec, Dusan - Filasova, Anna. “H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers”. International Journal of Applied Mathematics Electronics and Computers 3/2 (March 2015), 102-107. https://doi.org/10.18100/ijamec.47841.
JAMA Krokavec D, Filasova A. H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers. International Journal of Applied Mathematics Electronics and Computers. 2015;3:102–107.
MLA Krokavec, Dusan and Anna Filasova. “H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers”. International Journal of Applied Mathematics Electronics and Computers, vol. 3, no. 2, 2015, pp. 102-7, doi:10.18100/ijamec.47841.
Vancouver Krokavec D, Filasova A. H∞ Control of Continuous-Time Linear Systems Using Dynamic and Static Output Controllers. International Journal of Applied Mathematics Electronics and Computers. 2015;3(2):102-7.

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