Structure of linear systems: Geometric and transfer matrix approaches

The aim of this communication is to show how, depending on the type of the control law (static or dynamic), some fine structures (internal or input-output ones) have to be known precisely, since they completely characterize the solvability of control problems like decoupling, disturbance decoupling or model matching, . . . . These structures mainly describe zeros (finite and at infinity) and kernel indices. Both geometric and transfer matrix approaches are used in accordance with internal and external points of view.