An extended state observer for a class of nonlinear systems with a new frequency-domain analysis on convergence.

Regarding a class of multi-input and multi-output (MIMO) nonlinear systems, this paper presents a multi-variable linear extended state observer (MVLESO), which is applied to estimate uncertain dynamics of system real-timely. After that, a new frequency-domain analysis approach is explored to present the convergence property of MVLESO with respect to the estimation on uncertain dynamics. Meanwhile, the estimation error is mathematically modeled in frequency domain. Based on the as-built MVLESO, a robust dynamic inversion control (DIC) approach is put forward, and then it is applied to stabilize the attitude angular speeds of hypersonic vehicle. Simulation results show that, the proposed MVLESO can accurately estimate the time-varying uncertain dynamics in nonlinear system, and the deduced model about estimation error is also verified to be tenable. Furthermore, compared with the traditional DIC scheme, the MVLESO-based DIC scheme can stabilize the attitude angular speeds of researched vehicle more rapidly, and it can also possess stronger robustness against modeling uncertainties and structural disturbances.