On the multi input pole placement control problem

Feedback control of linear systems is efficiently made by the use of state space tools. It is well known that the use of an observer in combination with a state feedback gain generates linear time invariant closed loop systems with predetermined dynamics obtained by specifying a set of desired closed loop poles. In the present paper one of the cornerstones of this basic linear theory is discussed, The considered problem is to determine the feedback gains for multi input systems from a certain set of closed loop poles. The paper is a generalisation of the single input case for which there is a linear and unique correspondence between the closed loop poles and the gain. One such expression is known as Ackermann´s formula (1985). It is shown in the present paper how this feedback gain is generalised to the multi input case