Existence and robustness of minimal norm controllers

In this paper the possibility to stabilize linear discrete time-varying systems by state feedback is examined if the time dependency is totally unknown. We show that a minimum variance controller stabilizes the system in an optimal way in the sense that the norm of the closed-loop system matrix is minimized. We give some bounds for this minimal norm which can be easily calculated. Furthermore we present a method to calculate the sensitivity of the minimal norm if the controller is based on a small perturbation of the real system. At last a necessary and sufficient condition is given for the existence of a controller which with less control efforts than the minimum variance controller obtains the same minimal closed-loop norm.