Stabilization for Multirate Sampled-data Control Systems in case of Open-loop Unstable Plant

This paper proposes a stabilizing controller for the multirate sampled-data systems, which have a periodic output measurement scheme, in case of the open-loop unstable plant. A sufficient condition for maintaining observability in the multirate sampled-data systems is derived and a design strategy for filtered disturbance rejection is proposed. We also propose a design method for the plant output estimator. It is shown that the proposed pre-stabilizing controllers can stabilize the plant through the simulations. The proposed controller has IMC structure, and can be decomposed into the pre-stabilizing controller, the plant output estimator, the filtered disturbance estimator and the inverse of the fast pre-stabilized plant model. We assume that the plant is open-loop unstable and the disturbance consists of a sum of finite number of sinusoids with different frequencies. Some examples are presented for illustrations.