Consensus of multi-agent systems: a simultaneous stabilisation approach

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Abstract
This study considers the state consensus problem of multi-agent systems by virtue of novel simultaneous stabilisation techniques, where the distributed controller is proposed using relative outputs of the agents. A new consensus analysis condition is derived by studying the corresponding simultaneous stabilisation problem. Based on the analysis result, a necessary and sufficient condition is then established to ensure the consensus achievement of multi-agent systems, where the controller gain matrix is parameterised by a positive definite matrix, which is independent of the Lyapunov matrices. Iterative approaches are also developed to solve the design conditions, and to optimise the initial values with the solvability of the original problem improved. Further results are obtained for the dynamic output-feedback case. Finally, a numerical example is given to show the effectiveness of the obtained results.

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