Hybrid systems are dynamic systems where behavior is determined by interacting continuous and discrete dynamics. This paper considers the hybrid system models to be an extension of the discrete automata associating a continuous evolution with each discrete state. Such models are called hybrid automata. We introduce the coupled linear hybrid automaton. Next, we present an analytic formulation of its steady state behavior for the case where the discrete structure is a cycle. For the analyzed case, we establish sufficient and necessary conditions to attain a limit cycle. Finally, some of these results are applied in a specific class of systems.