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

We study the problem of disturbance decoupling with constant 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 and/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 satisfies the above invertibility condition, we use the special coordinate 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 contribution of these solutions is that the solutions are given in a set of linear equations. This resolves the well known difficulty in solving nonlinear equations associated with the DDPCM. When the invertibility condition is not satisfied, the solutions are characterized by a set of polynomial equations related to the obtained reduced-order system. This reduced-order characterization significantly simplifies the problem and reduces the computational cost in finding solutions to the DDPCM.