This paper considers the problem of designing a single static output feedback stabilizing controller for a finite set of linear systems. For this purpose, a set of square (equal number of inputs and outputs) minimum phase systems is considered. Using the notions of quadratic stabilizability, the existence of output feedback controller is derived in terms of the solvability of a set of matrix inequalities. Then the existence of the solution of such inequalities are derived for special class of systems. It is proved that a set of partially commutative or partially normal systems are stabilizable by a single static output feedback controller. These classes of systems are shown to be different from the well-known matched uncertain systems and considered to be new classes of systems. An algorithm is also presented to compute the controller gain.