Abstract
In this paper square Riccati matrix differential equations are considered. The coefficients can be arbitrary time—dependent matrices and need not satisfy any symmetry conditions. Contributions to the basic problems — existence and asymptotic behaviour of solutions — are presented based on two new methods. The first one is the usage of maximum principles for second order linear differential equations, the second one is a variety of possibilities for the parametric representation of solutions of Riccati differential equations.
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Freiling, G. and Jank, G.: Existence and Comparison Theorems for Algebraic Riccati Equations and Riccati Differential and Difference Equations, Schriftenreihe des Fachbereichs Mathematik der Universität Duisburg SM-DU-289, 1995.
Freiling, G. and Jank, G.: Non-Symmetric Matrix Riccati Equations, Z. Anal. Anwendungen, Vol. 14, No. 2, 1995.
Knobloch, H.W.: Differential Inequalities and Maximum Principles for Second Order Differential Equations, in: Nonlinear Analysis, Theory, Methods & Applications, Vol. 25, 1003–1016, 1995.
Reid, W.T.: Riccati Differential Equations, Academic Press, New York 1972.
Medanic, J.: Geometric Properties and Invariant Manifolds of the Riccati Equation, IEEE Trans. Automat. Contr. 27, No. 3, 1982.
Knobloch, H.W. and Kwakernaak, H.: Lineare Kontrolltheorie, Springer, Berlin 1985.
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Supported by Bundesministerium für Forschung und Technologie under grant 03-KN7WUE and the European Community under grant CHRX-CT94-0431
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Knobloch, H.W., Pohl, M. On Riccati Matrix Differential Equations. Results. Math. 31, 337–364 (1997). https://doi.org/10.1007/BF03322169
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DOI: https://doi.org/10.1007/BF03322169