Suppose that H1(s) and H2(s) are two strictly proper singleinput, single-output transfer functions with controllable statespace realizations (A1, B1, C1) and (A2, B2, C2), respectively. Construct a state-space realization for the parallel interconnection H1(s) H2(s), and use the Popov-Belevitch-Hautus eigenvector test to show that the parallel realization is controllable if and only if A1 and A2 have no common eigenvalues.

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