MULTIRATE CONTROL - A NEW APPROACH

A new multirate digital control of linear periodic and time-invariant systems is proposed. An explicit multirate law is given which transforms the overall control design into that of a relatively small-dimensional discrete time-invariant system for which standard design techniques can be used. It is shown that the proposed multirate scheme is, in general, more effective as a design tool than current multirate designs. The controllability properties of the multirate system are studied. Consequently, necessary and sufficient conditions for pole placement and stabilizability of the multirate system are given in terms of the continuous plant matrices. Moreover, the multirate LQR problem is solved. In this case, the solution is obtained by solving an algebraic discrete Riccati equation. Here, necessary and sufficient conditions for the existence of a unique nonnegative-definite solution of the Riccati equation and the asymptotic stability of the corresponding closed-loop multirate system are obtained. These conditions are given in terms of the continuous-time parameters.