Pole assignment by multirate sampled-data output feedback

Abstract 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 (nlttdot, nm) such that ≪(+n2+tdot+ m, equals the dimension of the state vector and the matrix b, [tdot A‴∼1b1tdot bmtdot A″ m∼ 'b] is non-singular. This capability gives a new perspective to the application of multirate sampled-data controllers.