Remarks on the periodic orbits of the matrix Riccati equation |
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Authors: | ENRIQUE SERNIK ARISTOTLE ARAPOSTATHIS |
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Affiliation: | Department of Electrical and Computer Engineering , The University of Texas at Austin , Austin, Texas 78712, U.S.A. |
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Abstract: | We investigate certain questions concerning the periodic structure of the matrix Riccati differential equation with constant coefficients. A closed-form expression for the periodic solutions is obtained for both the cases involving distinct or repeated eigenvalues in the associated linear hamiltonian system. Previous results are extended by establishing that periodic solutions are bounded if and only if the span of their range does not intersect the orthogonal complement of the controllable subspace of the associated linear system. |
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