Consensus of Networked Fractional-Order Systems With Intermittent Sampled Position Measurements

This paper investigates consensus of networked fractional-order systems over directed graph, with the networked double-integrator systems as its special case. An intermittent sampled position measurement distributed algorithm is proposed, which reduces the operation time and the update rates of controllers, and effectively responds to the circumstances if the information of agents' velocity and current position cannot be measured. In order to reach consensus, some necessary and sufficient conditions with respect to the fractional order, communication width, coupling gains, and networked structure, are derived by applying the fractional Laplace transform and stability theory. Note that consensus can be reached only if some inequalities are fulfilled, which serves as a guide for selecting the appropriate communication width and sampling period to reach consensus. Finally, some simulation examples are illustrated to verify the theoretical results.

Automated summary

This paper investigates consensus of networked fractional-order systems over directed graphs and proposes an intermittent sampled position measurement distributed algorithm to reduce operation time and update rates of controllers. It derives necessary and sufficient conditions for consensus using fractional Laplace transform and stability theory and emphasizes the importance of fulfilling certain inequalities to achieve consensus. Simulation examples are provided to verify the theoretical results.