Existence and robustness of minimal norm controllers

The possibility to stabilize linear discrete time-varying systems by state feedback is examined if the time dependency is totally unknown. The author shows 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. Some bounds for this minimal norm which can be easily calculated are given. Furthermore, a method is presented to calculate the sensitivity of the minimal norm if the controller is based on a small perturbation of the real system. 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