Stability of a certain class of hybrid dynamical systems

In this work we introduce a type of hybrid equation closely related to thos e that appear when a digital controller or a hybrid controller of a certain class is interconnected with a full non-linear continuous-time system. For these equations we obtain results concerning existence, uniqueness and non continuability of solutions. This results are used to study the behaviour o f the hybrid dynamical systems associated with those equations. We establis h relationships between the stability of these hybrid dynamical systems and the ones corresponding to their associated discretized systems on one hand , and to their associated linearized systems on the other. We also characte rize their stability, uniform asymptotic stability and exponential stabilit y. These results are applied to the exponential stabilization of a non-line ar control system by digital or hybrid controllers.