This article addresses the design of a nonlinear observer for nonlinear uncertain discrete‐time descriptor systems. The nonlinearities that appear in both state and output equations fulfill a Lipschitz‐like condition locally. Besides, the parametric uncertainties can affect the state dynamics as well as the input and output channels. The design methodology ensures input‐to‐state stability of the observer while minimizing an upper bound on a peak‐to‐peak performance index relating the disturbances/parametric uncertainties and the error in estimating a given performance signal. The observer design is cast as a convex optimization problem involving a set of linear matrix inequalities subject to a linear matrix equality constraint. The effectiveness of the proposed method is illustrated by numerical examples.

中文翻译：

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一类具有持续扰动的离散非线性奇异系统的鲁棒观测器设计

本文介绍了用于非线性不确定离散时间描述符系统的非线性观测器的设计。状态方程和输出方程中都出现的非线性局部满足Lipschitz类条件。此外，参数不确定性还会影响状态动态以及输入和输出通道。该设计方法可确保观察者的输入到状态稳定性，同时将与干扰/参数不确定性和估计给定性能信号的误差相关的峰峰值性能指标的上限最小化。将观察者设计转换为凸优化问题，该问题涉及一组受线性矩阵相等约束的线性矩阵不等式。数值例子说明了该方法的有效性。