On the problem of robust and perfect tracking for linear systems with external disturbances

We consider the robust and perfect tracking (RPT) problem for multivariable linear systems with external disturbances. The problem is to design a proper controller such that the resulting overall closed-loop system is asymptotically stable and the controlled output almost perfectly tracks a given reference signal with an arbitrarily fast settling time in the face of external disturbances and initial conditions. We derive a set of necessary and sufficient conditions under which the RPT problem is solvable. Under these solvability conditions, we develop algorithms for constructing state and output feedback laws, explicitly parameterized in ε, that solve the RPT problem. In our construction of feedback laws, we propose a controller structure which enables us to design a tracking controller without introducing additional integrators regardless what type the system is