Generalization of Ackermann´s formula for linear MIMO time invariant and time varying systems

This paper deals with the transformation of linear, multi-input-multi-output (MIMO) systems into Frobenius canonical form with the objective of introducing a new, computationally efficient methodology towards a desired pole-placement. Both time invariant and time-varying systems are considered with the classical formula of Ackermann (1972) generalized for both cases. This is the first such application of the formula in time-varying systems. This problem was disowned by many investigators due to its complexity in formulations. The advantage of the proposed technique is that it requires neither the coefficients of the characteristic polynomial or eigenvalues of the original system, nor the coefficients of the characteristic polynomial of the transformed system. The contribution of this effect to the numerical efficiency of pole placement is verified