A General Formula for Event-Based Stabilization of Nonlinear Systems

In this technical note, a universal formula is proposed for event-based stabilization of general nonlinear systems affine in the control. The feedback is derived from the original one proposed by E. Sontag in the case of continuous time stabilization. Under the assumption of the existence of a smooth Control Lyapunov Function, it is proved that an event-based static feedback, smooth everywhere except at the origin, can be designed so to ensure the global asymptotic stability of the origin. Moreover, the inter-sampling time can be proved not to contract at the origin. More precisely, it is proved that for any initial condition within any given closed set the minimal inter-sampling time is proved to be below bounded avoiding the infinitely fast sampling phenomena. Moreover, under homogeneity assumptions the control can be proved to be smooth anywhere and the inter-sampling time bounded below for any initial condition. In that case, we retrieve a control approach previously published for continuous time stabilization of homogeneous systems.