Abstract
In this paper, the positive state consensus problem of a network of homogeneous LTI positive agents is presented. A hierarchical control protocol is applied to achieve finite positive state consensus over directed networks. The minimal state-space realization considered for the interconnected positive agents is not restricted to be (internally) positive state-space realization, which is in contrast to the existing literature. A set of sufficient conditions is derived in linear programming framework which is solved to find controller gain matrices involved in the consensus protocol. Also, in this paper, an observer-based hierarchical control protocol has been derived to achieve finite positive state consensus. Numerical examples are given to demonstrate the usefulness of the proposed results.
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