Block triangular decoupling and pole assignment for linear systems over principal ideal domains

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A block triangular decoupling problem with static state feedback is studied for linear systems defined over a principal ideal domain with identity. First, basic properties of feedback reachability submodules are investigated, and then, under certain assumptions, necessary and sufficient conditions for the problem to be solvable are obtained. Furthermore, the pole assignability of the block triangularly decoupled system is discussed.

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