A Geometric Approach to Second-Order Consensus of Heterogeneous Networked Systems

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This paper investigates second-order consensus of networked systems with heterogeneous intrinsic nonlinear dynamics via a geometrical method, in which the nonlinear dynamics are governed by both velocity and position. First, two necessary conditions are deduced for the existence of consensus solutions by analyzing the inherent nonlinear dynamics of isolated nodes. Then a closed invariant set is constructed via geometrical methods. The nonempty of the set implies the existence of consensus solution. Assuming that the primary and the second dimension about the above invariant set are the same linear subspace, the system can be divided into two simple subsystems through a linear transformation. In addition, some sufficient conditions are proposed for reaching the global consensus based on matrix theory and Lyapunov method. Finally, numerical simulation results are provided to illustrate the validity of theoretical analysis.

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IEEE Transactions on Cybernetics