Two Applications for Hybrid H∞-Control: Generalised Sampled-Data and Loop-Shaping

Abstract

A hybrid general H∞ framework is presented, which can be applied to most linear control schemes, such as sampled-data control of time-varying systems, multirate sampling, mixed continuous-and discrete-time measurements and/or control signals as well as disturbance and performance signals. In infinite-time, the framework is specially emphasised on periodic systems. First necessary notations are introduced and the general hybrid framework is presented, and then the framework is applied to two different time-varying (periodic) systems. One is a generalised sampled-data system with no continuous-time measurements and control signals, however hybrid otherwise. The other corresponds to the well-known Glover-McFarlane loop-shaping design, with the advantage that there is no need for -ϒ-iterations.