Optimal control synthesis with prescribed closed loop poles

In this paper we propose an optimal controller synthesis method when a prescribed set of closed-loop poles is given. This technique relies on the specification of a closed-loop polynomial with degree greater than the minimal degree that ensures the existence of the pole-assignment equation solution. The degree difference generates an infinite number of solutions that correspond to non-minimal controllers. The set of free controller parameters are then chosen to optimize a H₂ cost function.