A Convex Characterization of Gain-Scheduled H∞ Controllers

An important class of linear time-varying systems consists of plants where the state-space matrices are fixed functions of some time-varying physical parameters `. Small Gain techniques can be applied to such systems to derive robust time-invariant controllers. Yet, this approach is often overly conservative when the parameters ` undergo large variations during system operation. In general, much higher performance can be achieved by control laws that incorporate available measurements of ` and therefore "adjust" to the current plant dynamics. This paper discusses extensions of H1 synthesis techniques to allow for controller dependence on time-varying but measured parameters. When this dependence is linear fractional, the existence of such gain-scheduled H1 controllers is fully characterized in terms of linear matrix inequalities (LMIs). The underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available. The formalism and derivatio..