Abstract
This paper considers the definitions of recursive and statelike representations form-D systems modeled as operators on a partially ordered Hilbert resolution space.
Using only the causality structure we develop a second-order transition representation which encompasses previously studied models. The same representation is shown to be valid for both quarter plane and arbitrary conic causality structures.
Transformation of the transition representation into a first-orderm-D local state model leads to the concept of structural minimality. We develop explicit conditions which apply to both stationary and nonstationary cases.
The transition representation also enables us to establish the existence of general 1-D wave advance model representations. Minimality of the wave advance model is also discussed.
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Supported in part by SDIO/IST and managed by ARO under Contract D24962-MA SDI.
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Aravena, J.L., Porter, W.A. State representations form-D systems with generalized causality structures. Math. Systems Theory 20, 155–168 (1987). https://doi.org/10.1007/BF01692063
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DOI: https://doi.org/10.1007/BF01692063