FEEDBACK DESIGN FOR MIMO NONLINEAR SYSTEMS: CHALLENGES, ROADBLOCKS, RECENT ADVANCES

Séance du mardi 21 novembre 2017, Salle V213, 09h45-11h00.

Alberto ISIDORI, University of Rome "La Sapienza", Italy

In this seminar, some challenging research problems dealing with the design of feedback law to control multi-input multi-output nonlinear (MIMO) systems are be reviewed. The seminar introduces a classification of MIMO systems based on certain properties of a generalized normal form that can be associated with an invertible system. Special cases are those systems that can be input-output linearized via state feedback, a special sub-case of which are systems that possess a vector relative degree. The focus of the seminar is on achieving (semiglobal) stability in the case of system that do not possess a vector relative degree. If the system is input-output linearizable it is possible, under the assumption of strong minimum-phase, to obtain semiglobal stability via dynamic output feedback. The design can be made robust to some extent. If the system is not input-output linearizable, semiglobal stability via dynamic output feedback can be obtained under the assumption that the zero dynamics are trivial and the system possesses a normal form in which states appear in a special triangular form. Apparently, such triangular form in some cases is intimately related to invertibility and (of course) to observability. The issue of (robust) stabilization in more general cases is still widely open.