A novel geometric insight into the model matching problem with stability

A novel approach to the model matching problem with internal stability is presented, completely embedded in the geometric approach framework. The exact model matching problem is posed as a measurable signal decoupling problem and a solution is developed, based on output dynamic feedback. The role played by the notions of multivariable relative degree, invariant zero structures and self-bounded controlled invariants is crucial in order to synthesize a minimum order compensator which guarantees internal stability, tracking with relative-degree delay, and - including the internal model - steady-state performance. The procedure herein detailed is easily extensible to nonminimum-phase systems and to non left-invertible systems. The results are presented for discrete-time systems, however they are also valid in the continuous-time case.