Basic properties of a class of rational matrix differential equations

2001 European Control Conference, ECC 2001

Volumn , Issue , 2001, Pages 2593-2598

  Freiling, G ^a   Hochhaus, A ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

34C10; 93E03; AMS Classification: 34A34

Indexed keywords

DIFFERENTIAL EQUATIONS;

34C10; 93E03; ALGEBRAIC EQUATIONS; RATIONAL MATRICES;

MATRIX ALGEBRA;

EID: 84947420152     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.2001.7076319     Document Type: Conference Paper

References (18)

1. Albert, A., "Conditions for positive and nonnegative definiteness in terms of pseudoinverses", SIAM J. Appl. Math. 17 (1969), 434-440.
2. Chen, S., Li, X., Zhou, X. Y., "Stochastic linear quadratic regulators with indefinite control weight costs", SIAM J. Control Optim. 36 (1998), 1685-1702.
3. Clements, D. J., Wimmer, H. K., "Monotonicity of the optimal cost in the discrete-time regulator problem and Schur complements", to appear.
4. Damm, T., Hinrichsen, D., "Newton's method for a rational matrix equation occuring in stochastic control", (Report 443, Institut für dynamische Systeme, Universit ät Bremen) (1999).
5. Dragan, V., Morozan, T., "Global solutions to a gametheoretic Riccati equation of stochastic control", J. Differential Equations 138 (1997), 328-350.
6. El Bouhtouri, A., Hinrichsen, D., Pritchard, A. J., "On the disturbance attenuation problem for a wide class of time invariant linear stochastic systems", Stochastics Stochastics Rep. 65 (1999), 255-297.
7. Fragoso, M. D., Costa, O. L. V., de Souza, C. E., "A new approach to linearly perturbed Riccati equations arising in stochastic control", Appl. Math. Optim. 37 (1998), 99-126.
8. Freiling, G., Hochhaus, A., "Properties of the solutions of rational matrix difference equations. Advances in difference equations, IV", Comput. Math. Appl., to appear.
9. Freiling G., Jank, G., "Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations", J. Dynam. Control Systems 2 (1996), 529-547.
10. Freiling, G., Jank, G., Abou-Kandil, H., "Generalized Riccati difference and differential equations", Linear Algebra Appl. 241/243 (1996), 291-303.
11. Hinrichsen, D., Pritchard, A. J., "Stochastic H∞", SIAM J. Control Optim. 36 (1998), 1504-1538.
12. Kolmanovskii, V. B., Richard, J.-P., "Some Riccati equations in the stability study of dynamical systems with delays", Neural Parallel Sci. Comput. 7 (1999), 235-252.
13. Lancaster, P., Tismenetsky, M., "The theory of matrices", Academic Press Inc., Orlando, 1985.
14. Reid, W. T., "Riccati differential equations", Academic Press, New York-London, 1972.
15. Verriest, E. I., "Robust stability and stabilization: from linear to nonlinear", Proc. IFAC Workshop, Ancona, 2000, 184-195.
16. Wimmer, H. K., "Monotonicity and maximality of solutions of discrete-time algebraic Riccati equations", J. Math. Systems Estim. Control 2 (1992), 219-235.
17. Wonham, W. M., "On a matrix Riccati equation of stochastic control", SIAM J. Control 6 (1968), 681-697.
18. Yong, J.; Zhou, X. Y. : Stochastic controls, Springer-Verlag, New York (1999).