Structural solvability of control problems the transfer matrix approach

The purpose of this paper is to present a survey on the structural solvability of some classical control problems such as decoupling and disturbance rejection by output measurement feedback within the transfer matrix approach. Graph-theoretic concepts are conjointly used with structural invariants to establish necessary and sufficient conditions for generic solutions of the above control problems. We deal with a particular class of parametrized systems called structured systems. These systems are closer to the physical reality and have a good description within the transfer matrix approach. Also, a graph characterization of the above-mentioned structural invariants is given. The necessary and sufficient conditions use the notion of input-output nodes disjoint paths in the graph associated with the system under study