Boundary Optimal Constant Control Versus Periodic Operation

One of the basic problems in Periodic Optimization is to ascertain by simple calculations whether the optimal constant control of a given plant can be improved by cycling or not. In this direction, one of the most powerful results is a frequency domain condition usually referred to as Π-criterion. The main limitation to the use of such a criterion is the assumption that the optimal constant control be an interior point of the admissible control set. In this paper, an extension of the Π-criterion to the case of boundary optimal constant control is presented and a particular case discussed in which the condition above can be given the useful form of a circle criterion.