Emerging as an effective control method, active disturbance rejection control technique (ADRC) can well deal with disturbances and uncertainties. Then focusing on the general nonlinear uncertain systems, this article illustrates the relation among stability, uncertainties, and parameters of linear ADRC controller when perturbation occurs in control input. On the one hand, if the reference and uncertainties satisfy particular conditions, the estimation and output errors are proved to be ultimately and globally bounded by Lyapunov function and Gronwall‐Bellman inequality, together with rigorous mathematical deducing and simulation verification. On the other hand, a globally and asymptotically stable result is obtained applying Lyapunov method and Cauchy inequality, and the convergence rate can be estimated when uncertainties exist. Besides, numerical simulations are carried out to fully display the correctness and dependability of results and proofs.

中文翻译：

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基于主动扰动抑制控制的非线性不确定系统的稳定性和收敛速度分析

主动干扰抑制控制技术（ADRC）逐渐成为一种有效的控制方法，可以很好地处理干扰和不确定性。然后，针对一般的非线性不确定系统，说明了当控制输入出现扰动时，线性ADRC控制器的稳定性，不确定性和参数之间的关系。一方面，如果参考和不确定性满足特定条件，则估计和输出误差最终会受到Lyapunov函数和Gronwall-Bellman不等式以及严格的数学推论和仿真验证的最终全局约束。另一方面，利用Lyapunov方法和Cauchy不等式获得了全局且渐近稳定的结果，并且当存在不确定性时可以估计收敛速度。除了，