Linear state-variable control laws with reduced-order observers may produce unstable feedback controllers

Prior to 1979, it was a commonly held belief among modern control researchers that a stabilizing linear feedback control law u=Kx/spl circ/, where x/spl circ/ is obtained from a state observer, would always produce a stable "controller" u(s)=G(s)/spl gamma/(s) for any completely controllable/observable linear plant x/spl dot/=Ax+Bu. However, in a 1979 paper it was proven that, in fact, the controller subsystem u(s)=G(s)/spl gamma/(s) of the stabilized closed-loop system x/spl dot/=Ax+BKx/spl circ/ may be unstable when a full-order observer is used to generate x/spl circ/. It is shown that the same possibility of controller instability also arises for the case when a reduced-order observer is used to generate x/spl circ/.