On the nonnegative self-adjoint solutions of the operator Riccati equation for infinite dimensional systems |
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Authors: | Frank M Callier Laurence Dumortier Joseph Winkin |
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Institution: | (1) Department of Mathematics, Facultes Universitaires Notre-Dame de la Paix, Rempart de la Vierge, 8, B-5000 Namur, Belgium |
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Abstract: | The nonnegative self-adjoint solutions of the operator Riccati equation (ORE) are studied for stabilizable semigroup Hilbert state space systems with bounded sensing and control. Basic properties of the maximal solution of the ORE are investigated: stability of the corresponding closed loop system, structure of the kernel, Hilbert-Schmidt property. Similar properties are obtained for the nonnegative self-adjoint solutions of the ORE. The analysis leads to a complete classification of all nonnegative self-adjoint solutions, which is based on a bijection between these solutions and finite dimensional semigroup invariant subspaces contained in the antistable unobservable subspace. |
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Keywords: | 93C05 93C25 47N70 47D06 47B65 49N10 |
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