Guaranteed stability for nonlinear systems by means of a hybrid loop

Abstract

We construct hybrid loops that augment continuous time control systems consisting in a continuous-time nonlinear plant in feedback with a (possibly non stabilizing) given nonlinear dynamic continuous-time controller. In particular, the arising hybrid closed-loops are guaranteed to follow the underlying continuous-time closed-loop dynamics when flowing and to jump in suitable regions of the closed-loop state space to guarantee that a positive definite function V of the closed-loop state and/or a positive definite function V_p of the plant-only state is non-increasing along the hybrid trajectories. Sufficient conditions for the construction of these hybrid loops are given for the nonlinear case and then specialized for the linear case with the use of quadratic functions. The proposed approach is illustrated on a linear and a nonlinear example.