The static output feedback existence criterion

The problem of finding criteria for the existence of stabilizing static output feedback for linear continuous stationary systems is considered. The fact is that the existing rank criteria for the existence of static state feedback are applicable only in cases where one of the input or output matrices has full rank. In all other cases, as a rule, frequent in practice, these criteria are not applicable. To solve the problem, a class of linear systems is introduced, for which a criterion for output feedback also exists and can be formulated as necessary and sufficient conditions. The main idea is to reduce the output matrix by means of a non-degenerate linear transformation to a certain block form.