Abstract
After providing an intrinsic definition of the adjoint system of a linear system given in state space form, we characterize the adjoint system in terms of the system’s external behavior. Conversely we show how this external characterization allows one to recover the state space definition by constructing an isomorphism from the abstractly defined minimal state space of the adjoint system to the dual of the minimal state space of the system itself. It is shown how a coordinate expression of this isomorphism can be obtained from a modified form of the Bezoutian matrix.
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