  In this paper, we analyse the impact of delayed event detection on the
stability of a 2-mode planar hybrid automata. We consider hybrid automata with
a unique equilibrium point for all the modes, and we find the maximum delay
that preserves stability of that equilibrium point. We also show for the class
of hybrid automata treated that the instability of the equilibrium point for
the equivalent hybrid automaton with delay in the transitions is equivalent to
the existence of a closed orbit in the hybrid state space, a result that is
inspired by the Joint Spectral Radius theorem. This leads to an algorithm for
computing the maximum stable delay exactly. Other potential applications of our
technique include co-simulation, networked control systems and delayed
controlled switching with a state feedback control.
