Direct Determination of Controller Parameters in Adaptive Pole Placement

For single-input single-output linear time-invariant discrete-time systems, a simple procedure is given for directly determining the controller parameters in adaptive pole placement. The given system is not required to be minimum phase. The only assumption on the system model is that the minimal order of the system is known a priori. The controller parameters are estimated using a standard recursive least squares algorithm. If an expanded regression vector is sufficiently exciting (as opposed to persistently exciting), the closed-loop system is exponentially stable with the closed-loop poles located close to the desired poles in the limit.