| Title:
|
On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate (English) |
| Author:
|
Jódar, Lucas |
| Author:
|
Navarro, E. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
6 |
| Year:
|
1989 |
| Pages:
|
429-438 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Cauchy problem |
| Keyword:
|
two-point boundary value problem |
| Keyword:
|
generalized matrix differential equations |
| Keyword:
|
generalized algebraic Riccati equation |
| Keyword:
|
error estimates |
| MSC:
|
15A06 |
| MSC:
|
15A24 |
| MSC:
|
34A05 |
| MSC:
|
34A45 |
| MSC:
|
34B99 |
| MSC:
|
65F30 |
| MSC:
|
65F99 |
| MSC:
|
65K10 |
| MSC:
|
65L05 |
| MSC:
|
65L10 |
| MSC:
|
93C15 |
| idZBL:
|
Zbl 0695.65050 |
| idMR:
|
MR1026507 |
| DOI:
|
10.21136/AM.1989.104373 |
| . |
| Date available:
|
2008-05-20T18:37:46Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104373 |
| . |
| Reference:
|
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| Reference:
|
[2] R. Brockett: Finite Dimensional Linear Systems.John Wiley, New York, 1970. Zbl 0216.27401 |
| Reference:
|
[3] J. Dieudonné: Foundations of Modern Analysis.Academic Press, New York. MR 0349288 |
| Reference:
|
[4] N. Dunford J. Schwartz: Linear Operators, Vol. I.Interscience. New York, 1957. |
| Reference:
|
[5] J. Eisenfeld: Operator equations and nonlinear eigenparameter problems.J. Functional Analysis, 12 (1973), 475-490. Zbl 0255.47018, MR 0350474, 10.1016/0022-1236(73)90007-4 |
| Reference:
|
[6] G. H. Golub C. F. Van Loan: Matrix Computations.North Oxford Academic, Oxford 1983. |
| Reference:
|
[7] V. Hernández L. Jódar: Sobre la ecuación cuadrática en operadores $A + BT + TC + TDT=0.Stochastica. Vol. VII, no 2 (1983), 145-154. MR 0766697 |
| Reference:
|
[8] V. Hernández L. Jódar: Boundary problems and periodic Riccati equations.IEEE Trans. Autom. Control, Vol. AC-30, No. 11 (1985), 1131-1133. MR 0810316, 10.1109/TAC.1985.1103831 |
| Reference:
|
[9] L. Jódar: Boundary problems for Riccati and Lyapunov equations.Proc. Edinburgh Math. Soc. 29 (1986), 15-21. MR 0829176 |
| Reference:
|
[10] L. Jódar: Explicit solutions for Sturm Liouville operator problems.Proc. Edinburg Math. Soc., 30(1987), 301-309. MR 0892699 |
| Reference:
|
[11] L. Jódar: Boundary value problems for second order operator differential equations.Linear Algebra and its Appls., 83 (1986), 29-38. MR 0862730 |
| Reference:
|
[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. MR 0888475 |
| Reference:
|
[13] H. Kuiper: Generalized Operator Riccati equations.SIAM J. Math. Anal., Vol. 16 (1985), 675-694. Zbl 0577.34053, MR 0793914, 10.1137/0516051 |
| Reference:
|
[14] K. Martensson: On the matrix Riccati equation.Inf. Sci. 3 (1971), 17-49. Zbl 0206.45602, MR 0280512, 10.1016/S0020-0255(71)80020-8 |
| Reference:
|
[15] G. G. L. Meyer H. J. Payne: An iterative method of solution of the algebraic Riccati equation.IEEE Trans. Aut. Control, (1972). MR 0451679 |
| Reference:
|
[16] J. D. Roberts: Linear Model Reduction and solution of the algebraic Riccati equation by use of the sign function.Int. J. Control, Vol. 32, No. 4 (1980), 677-687. Zbl 0463.93050, MR 0595962, 10.1080/00207178008922881 |
| . |
