State difference feedback can stabilize uncertain steady states

The present paper 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 paper conversely shows that the state difference feedback can stabilize just if the exclusion condition is not true. The ability of the method is illustrated by using a cart-pendulum system which moves along a one dimensional varying slope.