On the simultaneous stabilization of three or more plants

In this note, the problem of the simultaneous stabilization of three multivariable plants is addressed. We consider the general case where the existence of a unit controller cannot be used as a sufficient condition to guarantee the existence of a simultaneous controller for three multivariable plants. The sufficient conditions given in this note lead to a constructive controller design to stabilize simultaneously three multivariable plants. A generalization is proposed for stabilizing simultaneously n multivariable plants