Improving the performance of semiglobal output controllers for nonlinear systems

summary:For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers $(\mathcal{U}_R)_{R>0}$ with increasing regions of attraction $(\Omega_R)_{R>0}$ is that, when the region of attraction $\Omega_R$ is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is equal to some "fast" controller $\mathcal{U}_{R_0}$ on a neighborhood of the origin. Under an input-output-to-state stability (IOSS) assumption, we propose a new semiglobal stabilizing hybrid feedback controller that unifies a "slow" controller that has a large region of attraction with a "fast" controller having a small region of attraction. This unification is inspired from the elegant hybrid unification of a local controller with a global one given in [21]. Moreover, this unification is different from the recent result [24], since in the cited paper the objective is just the stabilization; whereas in our study, the objective is the stabilization with high performance. Finally, we illustrate our main result by means of two numerical examples