Modeling and analysis of time invariant linear hybrid systems

This paper outlines some preliminary work on the analysis of continuous coupled linear hybrid systems. We introduce the time invariant linear hybrid automaton. We establish an analytic formulation of its steady state behavior for the case where the discrete structure is a cycle. We obtain the "clock translation" basis for this case. Finally, we show our preliminary work on the existence and uniqueness conditions of the steady state in the noncoupled case.