Conclusion

This article deals with hybrid dynamical systems, from their modeling to stability conditions based on the use of Lyapunov functions. A thorough understanding of the solutions and stability concepts associated with this class of system is a prerequisite for their study. The results are based on basic assumptions about stability conditions: the flow and jump functions (f and g) are continuous; the flow and jump sets ( $\mathcal{C}$ and $\mathcal{D}$ ) are closed. The notion of maximal and complete solution also plays an important role.

As with non-linear systems, it has been shown that, in general, solutions do not simply converge to an equilibrium point...