Couple-group L2-L∞ Consensus of Nonlinear Multi-agent Systems with Markovian Switching Topologies

The paper is devoted to the couple-group L2-L∞ consensus problem of nonlinear multi-agent systems affected by external disturbances. The interaction topologies among agents obey a continuous-time Markovian process with unknown transition probabilities. By a system transformation, the problem of couple-group L2-L∞ consensus is converted into a L2-L∞ control issue. Then, by Lyapunov stability theory and graph theory, sufficient conditions for the couple-group L2-L∞ consensus are obtained. The control gains can be acquired via the solutions of a group of linear matrix inequalities. Moreover, the present method is extended to the multi-group L2-L∞ consensus. Finally, an example is provided to illustrate the effectiveness of the results.