In this paper, the simultaneous stabilization problem isconsidered using the matrix inequality approach. Some necessary andsufficient conditions for simultaneous stabilizability of r strictly propermulti-input/multi-output (MIMO) plants via static output feedback andstate feedback are obtained in the form of coupled ARI's. It is shown thatany such stabilizing feedback gain is the solution of some coupled linearquadratic control problems where every cost functional has a suitablecross term. A heuristic iterative algorithm based on the linear matrixinequality (LMI) technique is presented to solve the coupled matrixinequalities. The effectiveness of the approach is illustrated by numericalexamples.