On the finite time control of linear systems by piecewise constant output feedback†

The problem of finite time controllability of linear time invariant systems by piecewise constant output feedback is considered. It is shown that complete controllability and complete observability are both necessary and sufficient conditions for output feedback controllability by piecewise constant gain. Dead-beat output feedback controllers that drives the system to the origin in at most (μd × vd) steps, are also presented, where μd and vg are the indices of controllability and observability.