Multivariable regulation in geometric terms: Old and new results

The aim of this lecture is to present some well-known and some new results in multivariable regulation in a strictly geometric framework, each compared with the corresponding single-variable result approached with the standard transfer function techniques. It consists of three parts, each necessary for a clear presentation of the subsequent one: a selection of the basic tools, a survey of the solution of the asymptotically robust autonomous regulator problem with the internal model of the exosystem, and a presentation of the “steering along zeros technique” to obtain multivariable perfect tracking in the minimum-phase case or almost perfect tracking by using preaction in the nonminimum-phase case.