  We investigate stability of a solution of a hybrid system in the sense that
the graphs of solutions from nearby initial conditions remain close and tend
towards the graph of the given solution. In this manner, a small
continuous-time mismatch is allowed between the jump times of neighbouring
solutions and the `peaking phenomenon' is avoided. We provide conditions such
that this stability notion is implied by stability with respect to a
specifically designed distance-like function. Hence, stability of solutions in
the graphical sense can be analysed with existing Lyapunov techniques.
