Data-Driven Disturbance Decoupling Problem

In this letter, a data-driven solution to the disturbance decoupling problem (DDP) is provided. The required data consists of initial conditions, input, and output which is assumed to be corrupted by an unknown disturbance signal. A criterion is derived to check solvability of DDP just using the experimental (noisy) data. Further, data-driven computation of the largest controlled invariant subspace contained in the kernel of the output matrix is provided. The necessary state feedback matrices (often called friends of this subspace) for solving the DDP, are also computed using the experimental (noisy) data. In the process, several novel equivalent conditions for solvability of DDP are also established.