Geometric techniques for robust stabilization of linear time-varying systems

The foundation of a geometric theory for robust stabilization of infinite-dimensional time-varying linear systems is presented. The uncertainty of a system is described by perturbations of its graph and measured in the gap metric. An explicit expression for the radius of the maximal uncertainty in the plant that a feedback system can tolerate is given. The least amount of combined uncertainty that causes the feedback system to become unstable when uncertainty is present in both the plant and the controller is characterized. The fundamental mathematical object in this study is the parallel projection operator onto the graph of the plant along the inverse graph of the controller