Distributed observer for full-measured nonlinear systems based on knowledge of FMCF

Driven by practical applications, the achievement of distributed observers for nonlinear systems has emerged as a crucial advancement in recent years. However, existing theoretical advancements face certain limitations: they either fail to address more complex nonlinear phenomena, rely on hard-to-verify assumptions, or encounter difficulties in solving system parameters. Consequently, this paper aims to address these challenges by investigating distributed observers for nonlinear systems through the full-measured canonical form (FMCF), which is inspired by full-measured system (FMS) theory. To begin with, this study addresses the fact that the FMCF can only be obtained through the observable canonical form (OCF) in existing FMS theories. The paper demonstrates that a class of nonlinear systems can directly obtain FMCF through state space equations, independent of OCF. Also, a general method for solving FMCF in such systems is provided. Furthermore, based on the FMCF, A distributed observer is developed for nonlinear systems under two scenarios: Lipschitz conditions and open-loop bounded conditions. The paper establishes their asymptotic omniscience and demonstrates that the designed distributed observer in this study has fewer design parameters and is more convenient to construct than existing approaches. Finally, the effectiveness of the proposed methods is validated through simulation results on Van der Pol oscillators and microgrid systems.