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Pole assignment in the regular row-by-row decoupling problem

In this talk we discuss pole assignment in the regular row-by-row decoupling problem by applying the canonical decomposition of the right invertible system $\{C, A, B\}$ obtained in Wei, Cheng and Wang (2010a). When the regular row-by-row decoupling problem is solvable, we first derive the formulas of all solutions of the regular row-by-row decoupling problem, then derive a matrix $\mathcal{D}$ and prove that the system is controllable, if and only if $\rank(\mathcal{D})=l$, where $l$ is a parameter obtained in the canonical decomposition. We then define so called decoupling controllable vectors, with different cases of $\rank(\mathcal{D})$ and the dimension of the decoupling controllable vector subspace, characterize all attainable transfer function matrices for the decoupling and pole assignment problem.