Solutions to disturbance decoupling problem with constant measurement feedback for linear systems

Abstract

We study in this paper the problem of disturbance decoupling with constant (i.e., static) measurement feedback (DDPCM) for linear systems. For a class of systems which have a left invertible transfer function from the control input to the controlled output or a right invertible transfer function from the disturbance input to the measurement output, we obtain a complete characterization of all solutions to the DDPCM. For a system that does not satisfy the above invertibility condition, we use the special co-ordinate basis to obtain a reduced-order system. Then a complete characterization of all possible solutions to the DDPCM for the given system can be explicitly obtained, if the obtained reduced-order system itself satisfies the invertibility condition. The main advantage of these solutions is that the solutions are given in a set of linear equations. This resolves the well known difficulty in solving non-linear equations associated with the DDPCM.