Generalization of Ackermann's formula for state-feedback of multi-input systems

This note gives an alternate derivation of generalized Ackermann's formula (GAF). Proposed derivation extends the existing Ackermann' s gain formula to multi -input systems. Final result of the paper is obtained by the application of Cayley-Hamilton theorem. We propose two additional variations of Ackermann's gain formula. These formulae contain additional degrees of freedom which can be utilized to meet additional requirements along with placing all the poles at the desired locations. Paper also suggests different ways to overcome numerical difficulties while using the proposed formulae for gain computation.