Reset passivation of nonlinear controllers via a suitable time-regular reset map

For a class of square continuous-time nonlinear controllers we design a suitable resetting rule inspired by the resetting rule for Clegg integrators and First Order Reset Elements (FORE). With this rule, we prove that the arising hybrid system with temporal regularization is passive in the conventional continuous-time sense with a small shortage of input passivity decreasing with the temporal regularization constant. Based on the passivity property, we then investigate the finite gain stability of the interconnection between this passive controller and a passive nonlinear plant