Simultaneous stabilization via static output feedback and state feedback

In this paper, the simultaneous stabilization problem is considered using the matrix inequality approach. Some necessary and sufficient conditions for simultaneous stabilizability of strictly proper multi-input/multi-output (MIMO) plants via static output feedback and state feedback are obtained in the form of coupled algebraic Riccati inequalities. It is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term. A heuristic iterative algorithm based on the linear matrix inequality technique is presented to solve the coupled matrix inequalities. The effectiveness of the approach is illustrated by numerical examples.