Robust iterative learning control of continuous delayed singular multi-agent systems with polytopic uncertainty and non-identical initial conditions: LMI approach

Abstract

This paper addresses the leader-follower control problem for continuous delayed singular multi-agent systems (DSMAS) with uncertainties. This issue is particularly challenging due to the presence of polytopic uncertainty and independent initial conditions. To overcome these challenges, we propose a robust iterative learning control (RILC) with a rectified reference strategy for the DSMAS. The novelty of our approach lies in the introduction of the RILC, which deals with polytopic uncertainty, different independent initial conditions, and ensures monotonic convergence of the input in the 2-norm sense for the DSMAS, simultaneously. To establish stability, we derive sufficient criteria using the performance index and Lyapunov–Krasovskii functional and determine the RILC gains through linear matrix inequalities (LMIs). Finally, the proposed theory is validated through both numerical and practical examples, with simulation results demonstrating its capability and effectiveness.