On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate

Lucas Jódar; Enrique A. Navarro

Aplikace matematiky (1989)

  • Volume: 34, Issue: 6, page 429-438
  • ISSN: 0862-7940

Abstract

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In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic one.

How to cite

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Jódar, Lucas, and Navarro, Enrique A.. "On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate." Aplikace matematiky 34.6 (1989): 429-438. <http://eudml.org/doc/15598>.

@article{Jódar1989,
abstract = {In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic one.},
author = {Jódar, Lucas, Navarro, Enrique A.},
journal = {Aplikace matematiky},
keywords = {Cauchy problem; two-point boundary value problem; generalized matrix differential equations; generalized algebraic Riccati equation; error estimates; Cauchy problem; two-point boundary value problem; generalized matrix differential equations; generalized algebraic Riccati equation; error estimates},
language = {eng},
number = {6},
pages = {429-438},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate},
url = {http://eudml.org/doc/15598},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Jódar, Lucas
AU - Navarro, Enrique A.
TI - On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 6
SP - 429
EP - 438
AB - In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic one.
LA - eng
KW - Cauchy problem; two-point boundary value problem; generalized matrix differential equations; generalized algebraic Riccati equation; error estimates; Cauchy problem; two-point boundary value problem; generalized matrix differential equations; generalized algebraic Riccati equation; error estimates
UR - http://eudml.org/doc/15598
ER -

References

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  2. R. Brockett, Finite Dimensional Linear Systems, John Wiley, New York, 1970. (1970) Zbl0216.27401
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  7. V. Hernández L. Jódar, [unknown], Stochastica. Vol. VII, no 2 (1983), 145-154. (1983) MR0766697
  8. V. Hernández L. Jódar, 10.1109/TAC.1985.1103831, IEEE Trans. Autom. Control, Vol. AC-30, No. 11 (1985), 1131-1133. (1985) MR0810316DOI10.1109/TAC.1985.1103831
  9. L. Jódar, Boundary problems for Riccati and Lyapunov equations, Proc. Edinburgh Math. Soc. 29 (1986), 15-21. (1986) MR0829176
  10. L. Jódar, Explicit solutions for Sturm Liouville operator problems, Proc. Edinburg Math. Soc., 30(1987), 301-309. (1987) MR0892699
  11. L. Jódar, Boundary value problems for second order operator differential equations, Linear Algebra and its Appls., 83 (1986), 29-38. (1986) MR0862730
  12. L. Jódar, Boundary value problems and Cauchy problems for the second order Euler operator differential equation, Linear Algebra and its Appls., 91 (1987), 1-14. (1987) MR0888475
  13. H. Kuiper, 10.1137/0516051, SIAM J. Math. Anal., Vol. 16 (1985), 675-694. (1985) Zbl0577.34053MR0793914DOI10.1137/0516051
  14. K. Martensson, 10.1016/S0020-0255(71)80020-8, Inf. Sci. 3 (1971), 17-49. (1971) Zbl0206.45602MR0280512DOI10.1016/S0020-0255(71)80020-8
  15. G. G. L. Meyer H. J. Payne, An iterative method of solution of the algebraic Riccati equation, IEEE Trans. Aut. Control, (1972). (1972) MR0451679
  16. J. D. Roberts, 10.1080/00207178008922881, Int. J. Control, Vol. 32, No. 4 (1980), 677-687. (1980) Zbl0463.93050MR0595962DOI10.1080/00207178008922881

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