Some remarks on duality over a commutative ring |
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Affiliation: | Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), UMR CNRS 6597, 1 rue de la Noë BP 92 101, 44 321 Nantes Cedex 3, France |
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Abstract: | This paper addresses the duality problem for dynamical, linear, time-invariant systems defined over a ring. The duality principle is at the core of theoretical results for systems defined over a field, but this principle can not be applied for systems over a ring. From the definition of controlled and conditioned invariant submodules in the geometric approach, we analyze the relationships among various notions of invariance, using the concept of orthogonal submodule. These logical relations are summarized in two non-equivalent schemes. |
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