On a sufficient condition for static output-feedback multimodel control

This paper investigates a sufficient condition given by El Ghaoui (1993 ) for the simultaneous stabilization of a collection of linear time-invariant plants via static output-feedback control. Our main result shows that for square plants, with no purely imaginary transmission zeros, the sufficient condition will not hold if there is a plant with nonminimum phase transfer matrix G(s) or with singular high-frequency gain matrix lim_s→∞sG(s)