Non-weighted H∞ exponential output synchronization for time-delay heterogeneous multi-agent systems with switching topology via distributed observer compensation

Abstract

This paper studies the exponential $H_{\infty }$ output synchronization of time-delay heterogeneous multi-agent systems (TDHMASs) with switching topology. The TDHMAS simultaneously considers switching topology, node delay, and dimensional heterogeneity. Without directly using the information of the leader, a mode-dependent dynamic controller is designed based on each agent’s internal compensation term derived by a distributed observer for the leader. Unlike existing analysis techniques that designed mode-dependent Lyapunov–Krasovskii functionals (LKFs) jump high after each switching instant, our approach ensures the monotonic decrease of the designed LKF in the entire time domain, which essentially reduces the conservativeness of the results. The merits of methods in this paper are twofold: (a) It can be easily extended to non-weighted $H_{\infty }$ output synchronization of switched time-delay systems; (b) Both the observer gain and the controller gain of each mode are simultaneously designed by solving linear matrix inequalities (LMIs). Numerical simulations illustrate the advantages of our results, including the satisfactory estimation of the non-weighted $H_{\infty }$ performance compared to external disturbance and the monotonic decrease of the designed LKF.