Representation of multi-input-multi-output systems
Multi-input-multi-output systems

As with continuous single-input single-output systems, three types of representation are possible:

• by a transfer matrix, i.e. a matrix of transfer functions representing the transmittances between the various input-output pairs, u_i, y_j;

• by a system of differential equations linking the r outputs to the m inputs and their derivatives ;

• by a state model.

The transfer matrix is generally the basic model available when the system is too complex to be completely equated using the laws of physics, and a global input-output identification is required.

The second model, on the other hand, is the one we generally arrive at when the laws of physics (mechanics, electricity,...