Pole assignment by multirate sampled-data output feedback

Multirate sampled-data control of a linear time-invariant continuous-time plant is considered. It is shown that, if the plant is controllable and observable, we can always construct a multirate sampled-data gain controller such that the poles of the closed-loop system become a given symmetric set of n complex numbers (n is the dimension of the state vector of the plant). It is also shown that the input sampling rate {N1,...,Np} can be chosen equal to the Kronecker invariants or other "locally minimum controllability indices." This capability gives a new perspective to the application of multirate sampled-data controllers.