Discovery of Macrotarsomys bastardi at Beza Mahafaly Special Reserve, southwest Madagascar, with observations on the dynamics of small mammal interactions

Abstract

An important class of linear time-varying systems consists ofplants where the state-space matrices are fixed functions of sometime-varying physical parameters θ. Small gain techniques can beapplied to such systems to derive robust time-invariant controllers.Yet, this approach is often overly conservative when the parametersθ undergo large variations during system operation. In general,higher performance can be achieved by control laws that incorporateavailable measurements of θ and therefore “adjust” tothe current plant dynamics. This paper discusses extensions ofH∞ synthesis techniques to allow for controllerdependence on time-varying but measured parameters. When this dependenceis linear fractional, the existence of such gain-scheduled H∞ controllers is fully characterized in terms of linear matrixinequalities. The underlying synthesis problem is therefore a convexprogram for which efficient optimization techniques are available. Theformalism and derivation techniques developed here apply to both thecontinuous- and discrete-time problems. Existence conditions for robusttime-invariant controllers are recovered as a special case, andextensions to gain-scheduling in the face of parametric uncertainty arediscussed. In particular, simple heuristics are proposed to compute suchcontrollers