STRUCTURE AND OPTIMALITY OF MULTIVARIABLE PERIODIC CONTROLLERS

In this note we consider a linear periodic plant, to be controlled by measurement feedback. We analyze the general optimal synthesis problem where the objective is to select a compensator to minimize the norm o f the map between the controlled output and the exogenous input. It is shown that the performance of any linear compensator (possibly time v arying, nonperiodic) can be matched by a compensator contained in the restricted class of periodic controllers. This result is established i n the discrete-time case for bounded amplitude (l(infinity)) signals. In the continuous-time case the result is shown for bounded energy sig nals (L2, l2).