Balanced input-output assignment

Actuator/sensor locations and balanced representations of linear systems are considered for a given set of controllability and observability grammians. The case of equally controlled and observed states is given special attention. The assignability of grammians is examined, and the conditions for their existence are presented, along with several algorithms for their determination. Although an arbitrary positive semidefinite matrix is not always assignable, the identity grammian is shown to be always assignable. The results are extended to the case of flexible structures.