Simultaneous stabilization with near optimal H∞ performance

In this paper we consider the use of linear periodically time-varying (LPTV) controllers for simultaneous stabilization and disturbance rejection. Here we consider the case in which the control signal u does not appear directly in the output to be controlled (z) and the disturbance w does not appear directly in the measured output y. We prove that for every finite set of such plants for which the high-frequency gains (from u to y) satisfy a linear independence condition, we can design an LPTV controller which provides not only closed-loop stability, but also near optimal disturbance rejection in the H_∞ sense