Sampled disturbance decoupling with stability using multirate control

The sampled disturbance decoupling problem (SDDP) is considered for finite-dimensional linear systems. In this problem, a feedback control law is designed that eliminates the effect of an unknown disturbance on the output at specified sampling times. For discrete-time systems, the SDDP has a static-state feedback solution if and only if this feedback solves the standard disturbance decoupling problem (DDP). However, time-varying control laws can solve SDDP when it is not solvable by static-state feedback and, hence, when DDP cannot be solved. In particular, a technique for designing a periodically time varying multirate controller that solves SDDP is considered