Some new results on simultaneous stabilization controller using state-space approach

In this paper, the simultaneous stabilization problem for a set of MIMO plants is discussed and the necessary and sufficient condition for this problem is derived, It is shown that strong stabilization is equivalent to the existence of state feedback matrix F and state observation matrix H such that A+BF+HC+HDP is stable and that the simultaneous stabilizability of two plants is equivalent to finding two compatible state feedback matrix F_s and observation matrix H _s which is easily realized with computer and that simultaneous stabilizability of r+1 (r⩾2) plants is equivalent to simultaneous strong stabilizability r-1 associated plants together with a common stable subplant