Abstract
This brief works on the distributed adaptive consensus protocol design problem of heterogeneous linear networks over directed graphs. By introducing additive monotone increasing functions on both proportional and integral terms, a distributed adaptive consensus protocol is presented to achieve consensus. The property of $M$ -matrix is used to tackle the asymmetric Laplacian matrix of a directed graph. The protocols designed in this brief depend on only relative states of neighboring agents, requiring no global eigenvalue information of the graph, and thus can be implemented by each agent in a fully distributed fashion.
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