Stability analysis of a control system with nonlinear input uncertainty based on disturbance observer

In disturbance observer (DO)‐based control, control input attenuates a disturbance using observer output. Thus, the input may not achieve the attenuation if the input term includes uncertainty. Therefore, in order to correctly suppress the disturbance, it is essential to consider the uncertainty existing in the input term, and thus this article focuses on a nonlinear uncertainty in the input term. This article analyzes the stability and robustness of a DO‐based nonlinear control system with both the disturbance and the input uncertainty. We address the case that the disturbance and the uncertainty depend on time and states of a controlled system. The disturbance and the uncertainty are gathered in an integrated disturbance, and the integrated disturbance depends on many variables: the states, the control input, and the time. Therefore, a norm estimations for the disturbance and a time variation of the disturbance is difficult without knowledge of the state trajectory. Hence, a slope‐restriction for the disturbance is used for the stability analysis. Based on the mathematical analysis, we show input‐to‐state stability conditions due to extend the application class of the DO‐based controller to a control system with the disturbance and the nonlinear input uncertainty. The analytical results are verified by numerical simulations.