Event-based controller synthesis by bounding methods

Two event-triggered algorithms for digital implementation of a continuous-time stabilizing controller are proposed in this work. The first algorithm updates the control value in order to keep the time evolution of a given Lyapunov-like function framed between two auxiliary functions; whereas the second one actualizes the control value so that the state trajectory of the system stays enclosed between two a priori defined templates. In both cases, a natural hybrid formulation of the event-based stabilizing control problem is used to prove the main results of this work. Furthermore, the existence of a minimum inter-event time greater than zero is proved. Numerical simulations are provided to illustrate the digital implementation of the event-sampling algorithms for nonlinear systems.