Disturbance decoupling with stability and impulse-free response in singular systems

The problem of disturbance decoupling with stability and impulse-free response in square singular systems E x ̇ = Ax + Bu + Gq with output y = Dx, by applying a state feedback u = Fx, is considered. By employing Van Dooren's recursive algorithm for the computation of the subspace supremal (A, B)-invariant subspace in Kernel D and using Kalman's decomposition theorem, the paper's approach presents a complete solution to the underlying problem. Regarding state space systems, it is shown that the solution to the underlying problem is obtained almost directly from Van Dooren's recursive algorithm.