Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation

Sergej S. Vojtenko

Kybernetika (1987)

  • Volume: 23, Issue: 1, page 32-43
  • ISSN: 0023-5954

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Vojtenko, Sergej S.. "Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation." Kybernetika 23.1 (1987): 32-43. <http://eudml.org/doc/27928>.

@article{Vojtenko1987,
author = {Vojtenko, Sergej S.},
journal = {Kybernetika},
keywords = {antistabilizing solutions; nonautonomous matrix Riccati differential equation; optimal stabilization problem},
language = {eng},
number = {1},
pages = {32-43},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation},
url = {http://eudml.org/doc/27928},
volume = {23},
year = {1987},
}

TY - JOUR
AU - Vojtenko, Sergej S.
TI - Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation
JO - Kybernetika
PY - 1987
PB - Institute of Information Theory and Automation AS CR
VL - 23
IS - 1
SP - 32
EP - 43
LA - eng
KW - antistabilizing solutions; nonautonomous matrix Riccati differential equation; optimal stabilization problem
UR - http://eudml.org/doc/27928
ER -

References

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  1. W. T. Reid, Riccati Differential Equations, Academic Press, New York 1972. (1972) Zbl0254.34003MR0357936
  2. W. A. Coppel, Disconjugacy, Springer-Verlag, New York 1971. (1971) Zbl0224.34003MR0460785
  3. J. C. Willems, Least squares stationary optimal control and the algebraic Riccati equation, IEEE Trans. Automat. Control 16 (1971), 621-634. (1971) MR0308890
  4. V. Kučera, A review of the matrix Riccati equation, Kybernetika 9 (1973), 42-61. (1973) MR0328180
  5. H. Kwakernaak, R. Sivan, Linear optimal control systems, WileyTnterscience, New York 1972. (1972) Zbl0276.93001MR0406607
  6. B. D. O. Anderson, J. B. Moore, Linear optimal control, Prentice-Hall, Englewood Cliffs 1971. (1971) Zbl0321.49001MR0335000
  7. V. A. Jakubovich, Optimization and invariance of linear stationary control systems, Avtomatika i telemechanika 8 (1984), 5-41. In Russian. (1984) 
  8. R. E. Reid, al., An optimal controller arising from minimization of a quadratic performance criterion of indefinite form, IEEE Trans. Automat. Control 28 (1983), 985-987. (1983) Zbl0515.93026
  9. V. I. Zubov, Theory of optimal control, Sudostroenie, Leningrad 1966. In Russian. (1966) 
  10. V. I. Zubov, Lections in control theory, Nauka, Moscow 1975. In Russian. (1975) MR0406585
  11. D. L. Kleinman, On an iterative technique for Riccati equation computation, IEEE Trans. Automat. Control 13 (1968), 114-115. (1968) 
  12. W. M. Wonham, On a matrix Riccati equation of stochastic control, SIAM J. Control 6 (1968), 681-697. (1968) MR0239161
  13. M. Jamshidi, An overview of the solutions of the algebraic Riccati equation and related problems, Large Scale Systems 1 (1980), 167-192. (1980) MR0617986
  14. S. S. Vojtenko, E. J. Smirnov, Theory of optimal stabilization, Leningrad university, Leningrad 1983. In Russian. (1983) 
  15. S. S. Vojtenko, Universal iterative algorithm for the construction of maximal and minimalbounded solutions of the matrix Riccati equations, In: Algorithmy-85, zborník prednášek 8. sympozia o algorithmach, Vysoké Tatry -Štrbské Pleso, April 15-19, 1985, pp. 338-342. (1985) 

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