Parametrization of Linear Controllers for p-Dominance

Recently, the concept of p-dominance has been proposed as a unified framework to study rich behaviors of nonlinear systems. In this letter, we consider finding a set of linear dynamic output feedback controllers rendering the closed-loop systems p-dominant. We first derive an existence condition. Based on this condition, we then provide a parametrization of controllers. For Lure’s systems, the proposed method can be applied only by solving a finite family of linear matrix inequalities, which is illustrated by achieving multi-stabilization and stabilization of a limit cycle.