Pattern Preserving Pole Placement and Stabilization for Linear Systems

Abstract: A method to characterize the symmetries inherent within physical systems via automorphism groups has already been established. In this paper, we define a specific block diagonal form to which a matrix can be decomposed if and only if it conforms with a given set of symmetries. We employ this decomposition and resulting block diagonal form to define controllability and stabilizability and give a pole placement algorithm when the feedback matrix is constrained by the inherent patterns of the system. Finally, an example is given which demonstrates our controllability notion and pole placement algorithm.

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