Consensus of multi-agent systems on time scales

This paper studies consensus problems of multi-agent systems over a directed network topology on time scales. Based on the theory of time scales, we discuss continuous-time and discrete-time consensus protocols under a unified framework by employing a Lyapunov-like technique. We find that consensus can be realized exponentially if the graininess function of the time scale is bounded and the coupling strength of the network is sufficiently small. Many existing results of both continuous-time and discrete-time consensus conditions are shown to be special cases of this paper. Moreover, our derived results contain both continuous-time and discrete-time cases simultaneously. Finally, several illustrative examples are presented to show the effectiveness of the theoretical results.