LMI-based robust iterative learning control for leader–follower consensus of delayed singular heterogeneous multi-agent systems with uncertainties and initial shifts

This study deals with the leader–follower consensus for delayed singular heterogeneous multi-agent systems (DSHMASs) with norm-bounded uncertainties by proposing a robust iterative learning control (RILC) approach. The proposed RILC law guarantees zero-convergence of the tracking error despite norm-bounded uncertainties and unknown time-varying delays. Furthermore, it is shown that the control input vector achieves monotonic convergence under the L 2 -norm. A rectifying reference mechanism is employed to relax the requirement for identical initial conditions. Stability criteria are derived utilizing the performance index and Lyapunov–Krasovskii functional. The gains of the RILC are obtained by solving linear matrix inequalities (LMIs). Ultimately, the theoretical framework is verified via numerical and real-world examples, highlighting the method’s efficacy and robustness.