Continuous-time periodic systems in H 2 and H ∞ . Part I: Theoretical aspects

Patrizio Colaneri

Kybernetika (2000)

  • Volume: 36, Issue: 2, page [211]-242
  • ISSN: 0023-5954

Abstract

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The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of H 2 and H ∞ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in H 2 and H ∞ are introduced and solved.

How to cite

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Colaneri, Patrizio. "Continuous-time periodic systems in $H_2$ and $H_\infty $. Part I: Theoretical aspects." Kybernetika 36.2 (2000): [211]-242. <http://eudml.org/doc/33479>.

@article{Colaneri2000,
abstract = {The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of $H_2$ and $H_\infty $ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in $H_2$ and $H_\infty $ are introduced and solved.},
author = {Colaneri, Patrizio},
journal = {Kybernetika},
keywords = {periodic system; Riccati differential equation; periodic system; Riccati differential equation},
language = {eng},
number = {2},
pages = {[211]-242},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Continuous-time periodic systems in $H_2$ and $H_\infty $. Part I: Theoretical aspects},
url = {http://eudml.org/doc/33479},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Colaneri, Patrizio
TI - Continuous-time periodic systems in $H_2$ and $H_\infty $. Part I: Theoretical aspects
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 2
SP - [211]
EP - 242
AB - The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of $H_2$ and $H_\infty $ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in $H_2$ and $H_\infty $ are introduced and solved.
LA - eng
KW - periodic system; Riccati differential equation; periodic system; Riccati differential equation
UR - http://eudml.org/doc/33479
ER -

References

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  1. Bittanti S., Deterministic and stochastic linear periodic systems, In: Time Series and Linear Systems (S. Bittanti, ed.), Springer Verlag, Berlin 1986, pp. 141–182 (1986) MR0897824
  2. Bittanti S., Colaneri P., Nicolao G. De, The periodic Riccati equation, In: The Riccati equation (S. Bittanti, A. J. Laub, J. C. Willems, eds.), Springer Verlag, Berlin 1990, pp. 127–162 (1990) MR1132054
  3. Bolzern P., Colaneri P., The periodic Lyapunov equation, SIAM J. Matrix Analysis Appl. 4 (1998), 499–512 (1998) MR0964664
  4. Doyle J. C., Glover K., Khargonekaar P. P., Francis B. A., 10.1109/9.29425, IEEE Trans. Automat. Control 34 (1989), 831–846 (1989) MR1004301DOI10.1109/9.29425
  5. Mita T., Zhi L. Kang, Ohushi S., 10.1109/9.250489, IEEE Trans. Automat. Control 38 (1993), 343–347 (1993) MR1206827DOI10.1109/9.250489
  6. Colaneri P., Geromel J. C., Locatelli A., Control Systems Design – a H 2 and H ∞ Viewpoint, Academic Press, New York 1997 
  7. Bamieh B., Pearson J. B., 10.1109/9.126576, IEEE Trans. Automat. Control 37 (1992), 418–435 (1992) MR1153103DOI10.1109/9.126576
  8. Colaneri P., Hamiltonian systems and periodic Riccati equations in H 2 and H ∞ analysis and control of linear periodic systems, In: Proc. 30th Conference on Decision and Control, Brighton 1991, pp. 1914–1919 (1991) 
  9. Shayman M. A., 10.1137/0323045, SIAM J. Control Optim. 23 (1985), 27–32 (1985) Zbl0578.93051MR0798057DOI10.1137/0323045
  10. Xie L., Souza C. E. De, Fragoso M. D., 10.1016/0167-6911(91)90133-Y, Systems Control Lett. 17 (1991), 343–350 (1991) MR1136535DOI10.1016/0167-6911(91)90133-Y
  11. Colaneri P., Souza C. De, The H ∞ control problem for continuous-time linear periodic systems, In: Proc. of the IFAC Workshop on Systems Structure and Control, Prague 1992, pp. 292–295 (1992) 
  12. Limeeberg D. J., Anderson B. D. O., Khargonekar P. P., Green M., 10.1137/0330017, SIAM J. Control Optim. 30 (1992), 262–283 (1992) MR1149068DOI10.1137/0330017
  13. Ravi R., Nagpal K. M., Khargonekaar P. P., 10.1137/0329071, SIAM J. Control Optim. 29 (1991), 1394–1413 (1991) MR1132188DOI10.1137/0329071
  14. Chapellat H., Dahleh M., Bhattacharrya S. P., 10.1109/9.233174, IEEE Trans. Automat. Control 38 (1993), 1300–1303 (1993) Zbl0784.93052MR1235270DOI10.1109/9.233174
  15. Feintuch A., Khargonekar P., Tannenbaum A., 10.1137/0324064, SIAM J. Control Optim. (1986), 1076–1085 (1986) MR0854072DOI10.1137/0324064
  16. Basar T., Bernhard P., H ∞ Optimal Control and Related Minimax Design Problems, Birkhäuser, Basel 1991 MR1096294
  17. Colaneri P., Continuous–time periodic systems in H 2 and H ∞ – Part II: State–feedback problems, Kybernetika 36 (2000), No. 3 (to appear) MR1773508

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