r-CONSENSUS CONTROL FOR HIGHER-ORDER MULTI-AGENT SYSTEMS WITH DIGRAPH

This paper studies a consensus problem for lth (l >= 2) order multi-agent systems with digraph, namely, for a fixed r (0 <= r <= l - 1), the rth derivative x(i)(r) of the states x(i) of agents are convergent to a constant value and, for every k (0 <= k <= l - 1), x(i)(k) - x(j)(k) are convergent to zeros. A new concept of r-consensus is introduced and new consensus protocols are proposed for solving such an r-consensus problem. A sufficient and necessary condition for r-consensus is obtained. As special cases, criteria for third-order systems are given, in which the exact relationship between feedback gains is established. Finally, an illustrative example is given to demonstrate the effectiveness of these protocols.