General Choice of ES Dithers

Abstract

In this chapter we establish a simple and general extension of the previously developed bounded form of ES to a general class of oscillatory functions, including functions discontinuous with respect to time, such as triangle or square waves with dead time. We establish our main results by combining a novel idea for oscillatory control with an extension of functional analytic techniques originally utilized by Kurzweil, Jarnik, Sussmann, and Liu in the late 80 s and early 90s. We demonstrate the value of the result with an application to inverter switching control.