Regular linear systems and their reciprocals: applications to Riccati equations

For a regular linear system with zero in the resolvent set of the generator we introduce its reciprocal system, which has bounded generators. We show that there are close relationships between key system theoretic properties of such regular linear systems and their reciprocals. To illustrate the usefulness of this connection we give conditions under which their respective Riccati equations have the same self-adjoint bounded solutions.

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