Lossless H∞H∞-synthesis for 2D systems (special issue JCW)

We study 2D systems with a continuous and discrete time axis. We embed known results about the stability and H∞H∞-performance properties of such systems into multiplier theory from robust control. It is shown that this opens the way for applying recently developed gain-scheduled controller synthesis techniques in order to solve the H∞H∞-design problem for 2D systems without any conservatism. This is presented if the discrete-time axis is either one- or two-sided, the latter leading to non-conservative H∞H∞-synthesis result for infinite string interconnections of identical linear time-invariant systems.