Robust global stabilization of nonlinear systems by observer-based feedback controllers is a challenging task. This article investigates the problem of designing observer-based stabilizing controllers for incrementally quadratic nonlinear systems with external disturbances. The nonlinearities considered in the system model satisfy the incremental quadratic constraints, which are characterized by incremental multiplier matrices and encompass many common nonlinearities. The simultaneous search for the observer and the controller gain matrices is formulated as a feasibility problem of linear matrix inequalities, for two parameterizations (i.e., the block diagonal parameterization and the block antitriangular parameterization) of the incremental multiplier matrices, respectively. The closed-loop system implementing the observer-based feedback controller is proven to be input-to-state stable with respect to external disturbances. Using the proposed continuous-time observer-based controllers, event-triggered controllers with time regularization are constructed for globally Lipschitz systems, such that the closed-loop system is Zeno-free and input-to-state practically stable.

中文翻译：

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用于具有扰动的增量二次非线性系统的基于观测器的控制器


通过基于观测器的反馈控制器实现非线性系统的鲁棒全局稳定是一项具有挑战性的任务。本文研究了针对具有外部扰动的增量二次非线性系统设计基于观测器的稳定控制器的问题。系统模型中考虑的非线性满足增量二次约束，其特征在于增量乘数矩阵并包含许多常见的非线性。分别针对增量乘法器矩阵的两种参数化（即，块对角参数化和块反三角参数化），将观察者和控制器增益矩阵的同时搜索公式化为线性矩阵不等式的可行性问题。事实证明，实现基于观测器的反馈控制器的闭环系统对于外部干扰而言是输入状态稳定的。使用所提出的基于连续时间观测器的控制器，为全局 Lipschitz 系统构造了具有时间正则化的事件触发控制器，使得闭环系统是无 Zeno 的并且输入状态实际上是稳定的。