Abstract
We introduce a realization of the minimal state factorization for operators in Hilbert resolution spaces. Our realization identifies the minimal state with a subspace of the Hilbert space. The state trajectories are thenH-valued functions of time.
With the proposed realization we are able to prove continuity and bounded variation for the state trajectories. We also analyze factorization in the space of state trajectories and establish a three term factorization for the operator. The factorization represents all the dynamics as a map in the space of state trajectories.
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Aravena, J.L. State trajectories in Hilbert resolution spaces. Math. Systems Theory 19, 95–101 (1986). https://doi.org/10.1007/BF01704908
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DOI: https://doi.org/10.1007/BF01704908