Distributed Coordination of Fractional-order Systems with Extensions to Directed Dynamic Networks and Absolute/Relative Damping

This paper studies distributed coordination algorithms for multiple fractional-order systems under dynamic interaction and with absolute/relative damping. We first study a coordination algorithm in the case of a directed dynamic network topology. The convergence conditions on both the network topology and the fractional orders are presented. When the fractional-order alpha satisfies alpha is an element of ( 0, 1], necessary and sufficient conditions on the network topology are given to ensure coordination. When the fractional-order alpha satisfies alpha is an element of ( 1, 1 + 2/n), sufficient conditions on the network topology are given to ensure coordination. We then propose fractional-order coordination algorithms with absolute/relative damping and study the conditions on the network topology and the control gains such that coordination can be achieved under a directed fixed network topology. The final equilibria are also given explicitly.