Representation of Contractive Solutions of a Class of Algebraic Riccati Equations as Characteristic Functions of Maximal Dissipative Operators |
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Authors: | M. A. Nudelman |
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Affiliation: | (1) Integrated Banking Information Systems, P.O. Box 4, Uspenskaya 22, Odessa, 65014, Ukraine |
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Abstract: | Let I m is the identity matrix of order m. Let W(λ) be an entire matrix valued function of order 2m, W(0) = I 2m , the values of W(λ) are j mm -unitary at the imaginary axis and strictly j mm -expansive in the open right half-plane. The blocks of order m of the matrix W(λ) with appropriate signs are treated as coefficients of algebraic Riccati equation. It is proved that for any λ with positive real part this equation has a unique contractive solution θ(λ). The matrix valued function θ(λ) can be represented in a form θ(λ) = θ A (iλ) where θ A (μ) is the characteristic function of some maximal dissipative operator A. This operator is in a natural way constructed starting from the Hamiltonian system of the form with periodic coefficients. |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). Primary 34L05 Secondary 15A24 |
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