The new criteria of large dynamic system controlability and observability

The problem of controllability and observability analysis of a large linear dynamic MIMO-system with inputs and outputs not less than half the dimension of the state space is considered. New necessary and sufficient conditions (criteria) of the complete controllability and observability in the form of linear matrix inequalities are proposed. Based on these conditions, estimates are given for measures of controllability and observability. The example of analyzing the controllability of the large power system is given.