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

We consider in this paper 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 sys tem is asymptotically stable and the controlled output almost perfectly tra cks a given reference signal with an arbitrarily fast settling time in the face of external disturbances and initial conditions. The contribution of t his paper is two-fold: (1) We derive a set of necessary and sufficient cond itions under which the RPT problem is solvable; and (2) Under these solvabi lity conditions, we develop algorithms for constructing state and output fe edback laws, explicitly parameterized in epsilon, that solve the RPT proble m. In our construction of feedback laws, we propose a controller structure which enables us to design a tracking controller without introducing additi onal integrators regardless of what type the system is.