As the central component of active disturbance rejection control(ADRC), the performance analysis and evaluation on the linear extended state observer(LESO) and its extension case with higher extended order are of greatly significance. The convergence of the estimation error for LESO with any extended order is proved by utilizing Lyapunov’s inverse theory. Simultaneously, the quantitative relationship between the upper bound of the estimated error and the extended order is derived. Under the consideration of the given extended order, bandwidth and the shear frequency, the relationships between parameters of the observer and the dynamic response, and disturbance attenuation ability are both analyzed. Finally, combined with enhanced controller of ADRC, the performance evaluation and simulation verification on LESO and its extension case are carried out and discussed with respect to the capability in estimation, the suppression of peaking phenomenon and noise attenuation. The obtained conclusion can provide a theoretical basis for the selection of ESO in the application of ADRC.