Intersample ripple-free multirate H∞ optimal controller design

A systematic approach for the design of multirate controllers resulting in closed loops free of intersample ripple is proposed. The approach is particularly suited for design frameworks such as H optimal control for which previous proposed conditions to eliminate intersample ripple cannot be readily incorporated. It is based on transforming the control inputs in the lifted transfer matrix of the design plant in a manner that stabilizing controllers for the transformed plant are in one-to-one correspondence with stabilizing ripple-free controllers for the original plant. Thus, no solutions are lost in the process of this transformation and a general stability result is obtained that can be also used in other multirate controller design methodologies to achieve ripple-free response. The results do not require that the plant should be open-loop stable and in particular can contain integrating instabilities. Copyright (c) 2012 John Wiley & Sons, Ltd.