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Consensus-based Formation Control of Heterogeneous Linear Multi-agent Systems

This paper studies the formation control problem of heterogeneous linear multi-agent systems (MASs) with time-invariant relative position and angle constraints under a directed fixed communication topology. A consensus-based formation control protocol is proposed for the MAS based on the local information exchange between agents. First, we transform the formation control problem into the consensus problem. Then, the state linear transformation approach is used to further transform the consensus problem into the partial variable stability problem. Using the theory of partial variable stability, sufficient and necessary criteria are given to ensure the MAS realizes the required formation. In addition, the design process of the gain matrices in control protocol is given based on Lyapunov inequality and bilinear matrix inequality (BMI). Finally, a simulation example is presented to illustrate the validity of the theoretical results.