Disturbance decoupling of linear time-varying singular systems

The problem of disturbance decoupling by state feedback is defined for a linear time-varying singular system. It is required that the closed-loop system has a unique impulse-free solution and its output is not affected by disturbances. An algorithm, namely disturbance decoupling algorithm, is proposed. It is proved that the feasibility of the disturbance decoupling algorithm is invariant under any regular feedback control law. Based on the disturbance algorithm, a constructive method is provided to design a disturbance decoupling feedback control law. Sufficient conditions for the solvability of the disturbance decoupling problem are derived. It is proved that one of the sufficient conditions is also necessary provided that other conditions are satisfied.