New canonical form for pole placement

The bidiagonal-Frobenius form for single-input systems is presented. The new form is a compromise between the bidiagonal canonical form introduced by Policastro (1980) and the classical Frobenius one. It can be employed in the state-feedback pole-assignment problem, with the advantage that it requires neither the computation of the system eigenvalues as the bidiagonal form does, nor the characteristic polynomial coefficient evaluation as necessary using the Frobenius form. The final result is obtained using only the desired eigenvalues, and the coefficients of the feedback vector are given directly from the bidiagonal-Frobenius form without any computation.