On output static feedback: the addition of an extra relaxation constraint to obtain efficiently computable conditions

This paper is concerned with the use of output static feedback in linear time-invariant finite dimensional systems. We consider here the use of an extra relaxation constraint as a mean to obtain efficiently computable (sufficient) conditions for the synthesis of output static stabilizing controllers. We present novel necessary and sufficient conditions for output static feedback stabilizability, that are computable in terms of the solvability of a concave programming problem. We add an extra relaxation constraint to the above conditions, to define a new concept: output static stabilization in the relaxed sense. This (conservative) stabilization concept is fully characterized in terms of the LQR problem. The dependence of the above stabilization concept on the state-space representation of a system is analyzed. We show that for a particular class of plants, the stabilization problem in the above sense can be cast as a convex programming problem. We fully characterize a particular class of plants that are stabilizable in the above sense. A consequence of this characterization is somehow surprising: the identification of a class of plants stabilize via output static feedback, for which stabilizing feedback matrices can be (almost) expressed in analytic closed form. A result which is indeed a generalization of a well-known fact for SISO systems.