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Vojtenko, Sergej S.
Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation. (English). Kybernetika, vol. 23 (1987), issue 1, pp. 32-43
MSC: 34A12, 34A34, 34D05, 49D15, 93D20 | MR 883905 | Zbl 0623.34006
References:
[1] W. T. Reid: Riccati Differential Equations. Academic Press, New York 1972. MR 0357936 | Zbl 0254.34003
[2] W. A. Coppel: Disconjugacy. Springer-Verlag, New York 1971. MR 0460785 | Zbl 0224.34003
[3] J. C. Willems: Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans. Automat. Control 16 (1971), 621-634. MR 0308890
[4] V. Kučera: A review of the matrix Riccati equation. Kybernetika 9 (1973), 42-61. MR 0328180
[5] H. Kwakernaak, R. Sivan: Linear optimal control systems. WileyTnterscience, New York 1972. MR 0406607 | Zbl 0276.93001
[6] B. D. O. Anderson, J. B. Moore: Linear optimal control. Prentice-Hall, Englewood Cliffs 1971. MR 0335000 | Zbl 0321.49001
[7] V. A. Jakubovich: Optimization and invariance of linear stationary control systems. Avtomatika i telemechanika 8 (1984), 5-41. In Russian.
[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. Zbl 0515.93026
[9] V. I. Zubov: Theory of optimal control. Sudostroenie, Leningrad 1966. In Russian.
[10] V. I. Zubov: Lections in control theory. Nauka, Moscow 1975. In Russian. MR 0406585
[11] D. L. Kleinman: On an iterative technique for Riccati equation computation. IEEE Trans. Automat. Control 13 (1968), 114-115.
[12] W. M. Wonham: On a matrix Riccati equation of stochastic control. SIAM J. Control 6 (1968), 681-697. MR 0239161
[13] M. Jamshidi: An overview of the solutions of the algebraic Riccati equation and related problems. Large Scale Systems 1 (1980), 167-192. MR 0617986
[14] S. S. Vojtenko, E. J. Smirnov: Theory of optimal stabilization. Leningrad university, Leningrad 1983. In Russian.
[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.
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