Difference feedback can stabilize uncertain steady states

The present note is concerned with the stabilization of uncertain steady states by the state difference feedback. The feedback method has a peculiar feature that it uses only the difference between the present state x(t) and the past state x(t - T), considering exact information on the steady state is unavailable. Hitherto a condition is known under which such stabilization can not be realized. The present note conversely shows that the state difference feedback can stabilize just if the exclusion condition is not true. Furthermore a dynamic output difference feedback is shown to be able to stabilize under quite a mild condition that the steady state is not associated with zero eigenvalues. The ability of the method is illustrated by using a cart-pendulum system which moves along a one dimensional varying slope.