This article introduces a novel sliding mode observer design for sector bounded nonlinear systems. The proposed observer can simultaneously estimate both states and unknown parameters in the presence of disturbances and measurement noise. The observer is developed by using a time-averaged Lyapunov (TAL) functional to analyze the effect of noise (Gaussian) and to adequately reduce its effect on the system. The TAL averages the Lyapunov analysis over a small finite time interval, allowing for intuitive analysis of noises and disturbances acting on the system. The TAL is shown to satisfy all the requirements of a Lyapunov candidate function. The article focuses on the observer design for sector bounded nonlinear systems since several nonlinearities can be modeled using a sector bound. An optimization approach is also developed to provide a tight bound on the effect of the uncertainty on the estimated parameters. The conditions for the existence of the observer are presented in the form of linear matrix inequality (LMI), which can be explicitly solved offline using commercial LMI solvers. Furthermore, the LMI design is also extended to a specific case of a dissipative nonlinear system. The observer design has also been extended to the case where the input disturbance is correlated with the sensor noise.

中文翻译：

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扇区有界非线性系统的自适应滑模观测器

本文介绍了一种用于扇形有界非线性系统的新型滑模观测器设计。所提出的观测器可以在存在干扰和测量噪声的情况下同时估计状态和未知参数。观测器是通过使用时间平均李雅普诺夫 (TAL) 函数来分析噪声（高斯）的影响并充分减少其对系统的影响而开发的。TAL 在一个小的有限时间间隔内平均 Lyapunov 分析，允许对作用在系统上的噪声和干扰进行直观分析。TAL 被证明满足李雅普诺夫候选函数的所有要求。本文重点介绍扇区有界非线性系统的观测器设计，因为可以使用扇区边界对多个非线性进行建模。还开发了一种优化方法，以提供对不确定性对估计参数的影响的严格限制。观察者存在的条件以线性矩阵不等式 (LMI) 的形式表示，可以使用商业 LMI 求解器离线明确求解。此外，LMI 设计还扩展到耗散非线性系统的特定情况。观测器设计还扩展到输入干扰与传感器噪声相关的情况。LMI 设计还扩展到耗散非线性系统的特定情况。观测器设计还扩展到输入干扰与传感器噪声相关的情况。LMI 设计还扩展到耗散非线性系统的特定情况。观测器设计还扩展到输入干扰与传感器噪声相关的情况。