H∞ Consensus with a Time-Varying Reference State in Directed Multi-Agent Networks with Time-Varying Delays

This paper investigates consensus control with a time-varying reference state in directed multi-agent networks with time-varying delays and subject to external disturbances. The consensus problem is transformed into a H-infinity control problem by defining an appropriate controlled output. In addition, we propose consensus algorithms with a time-varying reference state, which can be an exogenous signal or evolve according to a nonlinear model. Furthermore, convergence analysis is conducted by constructing Lyapunov-Krasovskii function. Based on linear matrix inequalities (LMIs) techniques, sufficient conditions are given to guarantee multi-agent consensus with a time-varying reference state under the desired H-infinity performance index. Finally, simulation examples are given to demonstrate the effectiveness of the theoretical results.