Practical fixed-time observer-based generalized cascade predictor design for synchronization of integrator systems with delays and complex unknowns

This paper studies output feedback leaderless synchronization problem for high-order integrator chains subject to nonlinear dynamics, measurement noises, matched disturbances, and time delays in both input and output. First, we consider the varying normal-scale input delay case and propose a novel extended state observer (ESO)-based predictor device for each agent using relative output of neighbors. Then, in combination with integral sliding mode, leaderless fully distributed synchronization protocols are designed which can highly compensate for delays and unknowns. In particular, the ESO combines the transient performance of fixed-time algorithms with the continuous/smooth, anti-noise and low-cost strengths of linear algorithm via linear structure and time base gains. Also, any disturbances considered in this protocol are not generated by known exosystem and hence the proposed anti-disturbance time delay compensation scheme is more general. Second, aiming to cope with a larger class of input delays, the above device is extended to a ESO-based cascade predictor device. Synchronization analysis is placed in the Lyapunov-Krasovskii functional frame and sufficient conditions are deduced to ensure that the synchronization errors converge to a residual set in fixed time. Detailed numerical simulation studies and thorough comparisons are provided to verify the effectiveness and superiority of the designed ESO and devices.