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, a multirate sampled-data ‘gain‘ controller can always be constructed so that the poles of the closed-loop system become an arbitrarily-given symmetric set of complex numbers. It is also shown that the input sampling rate (JV,,[tdot],NJ can be chosen equal to the Kronecker invariants, or other locally minimum controllability indices. Here, ‘locally minimum controllability indices’ are defined as a set of integers (nlt[tdot], nm) such that ≪(+n2+[tdot]+ m, equals the dimension of the state vector and the matrix [b, [tdot] A‴∼1b1[tdot] bm[tdot] A″ m∼ 'b] is non-singular. This capability gives a new perspective to the application of multirate sampled-data controllers.