Direct algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case

This paper deals with the direct solution of the pole placement problem by statederivative feedback for multi-input linear systems. The paper describes the solution of this pole placement problem for any controllable system with nonsingular system matrix and nonzero desired poles. Then closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results into a formula similar to Ackermann one. Its derivation is based on the transformation of linear multi-input systems into Frobenius canonical form by coordinate transformation, then solving the pole placement problem by state derivative feedback and transforming the solution into original coordinates. The procedure is demonstrated on examples. In the present work, both time-invariant and time-varying systems are treated.