Bipartite consensus for a network of wave equations with time-varying disturbances

Abstract

This paper studies the consensus problem for a network of wave equations subject to antagonistic interactions and exogenous disturbances. To this end, a distributed boundary algorithm is proposed with the aid of infinite-dimensional observers. We first deal with the well-posedness of the underlying system. Then we show that the bipartite consensus problem can be solved. In addition, it is also illustrated that the negative effect induced by the boundary disturbances can be eliminated by virtue of the proposed algorithm. Finally, a numerical example is presented to support the derived results.