A comprehensive introduction to the geometric theory of linear multivariable systems

A simple tutorial introduction to the geometric theory of linear multivariable control is presented. This corresponds to approximately three two-hour lectures in a graduate-level course. The authors emphasise the intuitive control interpretation of the main geometric concepts. To this end, the authors focus interest on trajectory formulation for subspace invariance and discrete-time interpretation of the basic subspaces and their construction algorithms. Application of geometric theory for solving the disturbance decoupling problem is illustrated via two pedagogical examples