| Title:
|
A review of the matrix Riccati equation (English) |
| Author:
|
Kučera, Vladimír |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
9 |
| Issue:
|
1 |
| Year:
|
1973 |
| Pages:
|
(42)-61 |
| . |
| Category:
|
math |
| . |
| MSC:
|
15A24 |
| MSC:
|
34A99 |
| MSC:
|
49J99 |
| MSC:
|
93C15 |
| MSC:
|
93E10 |
| idZBL:
|
Zbl 0279.49015 |
| idMR:
|
MR0328180 |
| . |
| Date available:
|
2009-09-24T16:30:26Z |
| Last updated:
|
2012-06-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124651 |
| . |
| Reference:
|
[1] M. Athans P. L. Falb: Optimal Control.McGraw-Hill, New York 1966. MR 0204181 |
| Reference:
|
[2] R. W. Bass: Machine Solution of High-Order Matrix Riccati Equations.Douglas paper 4538. |
| Reference:
|
[3] R. Bellman: Dynamic Programming.Princeton University Press, Princeton, N. Y. 1957. Zbl 0995.90618, MR 0090477 |
| Reference:
|
[4] S. P. Bingulac M. R. Stojić N. Ćuk: On an Iterative Solution of Time-Invariant Riccati Equation.In: Prepr. JACC, St. Louis, Miss., 1971, 178-182. |
| Reference:
|
[5] T. R. Blackburn: Solution of the Algebraic Matrix Equation Via Newton-Raphson Iteration.In: Prepr. JACC, Ann Arbor, Mich., 1968, 940-945. MR 0247753 |
| Reference:
|
[6] R. W. Brockett: Finite Dimensional Linear Systems.John Wiley, New York 1970. Zbl 0216.27401 |
| Reference:
|
[7] A. E. Bryson, Yu-Chi Ho: Applied Optimal Control.Bleisdell, Waltham, Mass. 1969. |
| Reference:
|
[8] R. S. Bucy: Global Theory of the Riccati Equation.J. Comp. System Sci. 1 (December 1967), 4, 349-361. Zbl 0155.14403, MR 0229916 |
| Reference:
|
[9] R. S. Bucy P. D. Joseph: Filtering for Stochastic Processes with Applications to Guidance.Interscience, New York 1968. MR 0267946 |
| Reference:
|
[10] J. J. O'Donnell: Asymptotic Solution of the Matrix Riccati Equation of Optimal Control.In: Proc. 4th Ann. Allerton Conf. Circuit and Syst. Theory, Urbana, III., 1966, 577-586. |
| Reference:
|
[11] S. E. Dreyfus: Dynamic Programming and the Calculus of Variations.Academic Press, New York 1965. Zbl 0193.19401, MR 0199764 |
| Reference:
|
[12] A. F. Fath: Computational Aspects of the Linear Optimal Regular Problem.Trans. IEEE AC-14 (October 1968), 547-550. MR 0274131 |
| Reference:
|
[13] M. L. J. Hautus: Stabilization, Controllability and Observability of Linear Autonomous Systems.Nederl. Akad. Wetensch., Proc. Ser. A73 (1970), 448-455. Zbl 0212.47302, MR 0289170 |
| Reference:
|
[14] K. L. Hitz: Relations Between Continuous-Time and Discrete-Time Quadratic Minimization.Ph. D. Thesis, The University of Newcastle, Australia, 1970. |
| Reference:
|
[15] R. E. Kalman: Contributions to the Theory of Optimal Control.Bol. Soc. Mat. Max. J (1961), 102-119. MR 0127472 |
| Reference:
|
[16] R. E. Kalman: When Is a Linear Control System Optimal?.Trans. ASME, J. Basic Engr. 86D (March 1964), 51-60. |
| Reference:
|
[17] R. E. Kalman R. S. Bucy: New Results in Linear Prediction and Filtering Theory.Trans. ASME, J. Basic Engr. 83D (1961), 95-100. MR 0234760 |
| Reference:
|
[18] R. E. Kalman T. S. Englar: A Users Manual for the Automatic Synthesis Program.NASA Rept. CR-475, June 1966. |
| Reference:
|
[19] R. E. Kalman P. L. Falb M. A. Arbib: Topics in Mathematical System Theory.McGraw-Hill, New York, 1969. MR 0255260 |
| Reference:
|
[20] D. L. Kleinman: On the Linear Regulator Problem and the Matrix Riccati Equation.MIT Electronic Systems Lab., Cambridge, Mass, Rept. ESL-R-271, June 1966. |
| Reference:
|
[21] D. L. Kleinman: On an Iterative Technique for Riccati Equation Computations.Trans. IEEE AC-13 (February 1968), 114-115. |
| Reference:
|
[22] V. Kučera: A Contribution to Matrix Quadratic Equations.Trans. IEEE AC-17 (June 1972), 344-347. MR 0449830 |
| Reference:
|
[23] V. Kučera: On Nonnegative Definite Solutions to Matrix Quadratic Equations.In: Proc. 5th IFAC Congress Vol. 4, Paris, 1972. Also Automatica 7 (July 1972), 413-423. MR 0332827 |
| Reference:
|
[24] V. Kučera: The Discrete Riccati Equation of Optimal Control.Kybernetika 8 (1972), 430-447. MR 0332254 |
| Reference:
|
[25] J. J. Levin: On the Matrix Riccati Equation.Trans. Am. Math. Soc. 10 (1959), 519-524. Zbl 0092.07803, MR 0108628 |
| Reference:
|
[26] K. Mårtensson: On the Matrix Riccati Equation.Information Sci. 3 (1971), 1, 17-49. MR 0280512 |
| Reference:
|
[27] A. G. J. McFarlane: An Eigenvector Solution of the Linear Optimal Regulator Problem.J. Electron. Contr. 14 (June 1963). |
| Reference:
|
[28] B. P. Molinari: The Stabilizing Solution of the Matrix Quadratic Equation.To appear in SIAM J. Control 10 (1972). MR 0424309 |
| Reference:
|
[29] L. S. Pontryagin at al.: The Mathematical Theory of Optimal Processes.Interscience, New York 1961. |
| Reference:
|
[30] J. E. Potter: Matrix Quadratic Solutions.SIAM J. Appl. Math. 14 (May 1966), 3, 496-501. Zbl 0144.02001, MR 0201457 |
| Reference:
|
[31] J. D. Roberts: Linear Model Reduction and Solution of the Algebraic Riccati Equation by Use of the Sign Function.To appear in Trans. IEEE AC-17 (1972). MR 0595962 |
| Reference:
|
[32] A. P. Sage: Optimum Systems Control.Prentice-Hall, Englewood Cliffs, N. J. 1968. Zbl 0192.51502, MR 0255264 |
| Reference:
|
[33] V. Strejc: State Space Synthesis of Discrete Linear Systems.Kybernetika 8 (1972), 83-113. Zbl 0254.93028, MR 0337404 |
| Reference:
|
[34] D. R. Vaughan: A Negative Exponential Solution for the Matrix Riccati Equation.Trans. IEEE AC-14 (February 1969), 72-75. MR 0250727 |
| Reference:
|
[35] W. M. Wonham: On Pole Assignment in Multi-Input Controllable Linear Systems.Trans. IEEE AC-12 (December 1967), 660-665. |
| Reference:
|
[36] W. M. Wonham: On a Matrix Riccati Equation of Stochastic Control.SIAM J. Control 6 (1968), 4, 681-698. MR 0239161 |
| . |
