A CONVEX CHARACTERIZATION OF GAIN-SCHEDULED H-INFINITY 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 theta. 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 theta undergo large variations during system operation, In general, higher performance can be achieved by control laws that incorporate available measurements of theta and therefore ''adjust'' to the current plant dynamics. This paper discusses extensions of H-infinity, 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 H-infinity, controllers is fully characterized in terms of linear matrix inequalities. The underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available. The formalism and derivation techniques developed here apply to both the continuous- and discrete-time problems. Existence conditions for robust time-invariant controllers are recovered as a special case, and extensions to gain-scheduling in the face of parametric uncertainty are discussed. In particular, simple heuristics are proposed to compute such controllers.