Robust consensus control for a class of second-order multi-agent systems with uncertain topology and disturbances

In the paper, the robust consensus control is investigated for a class of second-order multi-agent systems with time-varying interaction topology and disturbances. Firstly, due to the variation considered being bounded, the topology is modeled as time-varyingly uncertain topology with polytopic type. Then, regarding the uncertain parameters as independent variables and formulating the multi-agent system as a special polynomial system, the robust consensus problem is converted to the robust stability analysis of the error model via stability theory of control systems. Furthermore, the idea is generalized to study the disturbance attenuation problem. Sufficient conditions for the solutions to the robust consensus problems without and with disturbance attenuation are formulated in terms of homogeneous parameter-dependent linear matrix inequalities (HPD-LMIs) which can be solved via semidefinite programming relaxations based on the sum of squares technique. Finally, simulation results are provided to illustrate the effectiveness of the approach.