Consensus of fractional-order systems with non-uniform input and communication delays

This paper studies the consensus problems of fractional-order systems with non-uniform input and communication delays over directed static networks. Based on a frequency-domain approach and generalized Nyquist stability criterion, sufficient conditions are obtained to ensure the consensus of the fractional-order systems with simultaneously non-uniform input and communication delays. When the fractional-order alpha subset of (0,1], it is found that the consensus condition is dependent on input delays but independent on communication delays. Surprisingly, when there is no input delay, consensus can be realized whatever the communication delays are. However, a counter-example shows that communication delays will have a great influence on the consensus condition when the fractional-order alpha is an element of (1,2). Moreover, the bounds of input and communication delays are explicitly given to guarantee the consensus of the delayed fractional-order systems with fractional-order alpha is an element of (0,2) under an undirected interaction graph.