Structure and optimality of multivariable periodic controllers

A linear periodic plant to be controlled by measurement feedback is considered. The general optimal synthesis problem in which the objective is to select a compensator to minimize the norm of the induced map between the controlled output and the exogeneous input is analyzed. It is shown that the performance of any linear compensator (possibly time varying, nonperiodic) can be matched by a compensator contained in the restricted class of periodic controllers. This result is established in the discrete-time case for bounded amplitude (l_∞ ) signals. In the continuous-time case the result is shown for bounded energy signals (L₂,l₂)