Uniting local and global controllers

We consider control systems for which we know two stabilizing controllers. The former is “optimal” but local, the latter is global. We look for a uniting control law providing a globally stabilizing locally optimal controller. We study several solutions based on continuous, discontinuous, hybrid, time varying controllers. One criterion of selection of a controller is the robustness of the global asymptotic stability to vanishing measurement noise. This leads us in particular to consider a kind of generalization of Krasovskii solutions for hybrid systems