Pole-placement for SISO linear systems by state-derivative feedback

A procedure for solving the pole-placement problem for a linear single-input/single-output (SISO) systems by state-derivative feedback is described. This pole-placement problem is always solvable for controllable systems if all eigenvalues of the original system are nonzero. Then any arbitrary closed-loop poles can be placed to achieve the desired system performance. The solution procedure results in a formula similar to the Ackermann one. Its derivation is based on the transformation of a linear SISO system into Frobenius canonical form by co-ordinate transformation, then solving the pole-placement problem by state-derivative feedback and transforming the solution into the original co-ordinates. The solution is also extended to time-varying systems.