Design of a stable state feedback controller based on the multirate sampling of the plant output

A new type of controller is proposed which detects the ith plant output N_i times during a period of T₀ and changes the plant inputs once during T ₀. It is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable. This implies, for instance, that arbitrary symmetric pole assignment is possible if the plant is controllable. It is also shown that, if the plant has no zeros at the origin, the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized. That is to say, inversely expressed, any state feedback can be equivalently realized by a controller with any prescribed degree of stability