H∞ dynamic observer design for a class of Lipschitz nonlinear discrete-time systems with time varying delays

Optimal Control Applications and Methods Pub Date : 2023-12-12 DOI:10.1002/oca.3081

Ghali Naami, Mohamed Ouahi

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Abstract

This study explores the development of

H_{\infty} $$ {H}_{\infty } $$

dynamic observer (HDO) for discrete-time nonlinear systems (DTNLS) with time-varying delay (TVD) and disturbances. The approach is to construct an augmented Lyapunov–Krasovskii function (LKF) with double summation terms, using the generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen-based inequality (JBI) and the Wirtinger-based inequality (WBI). These lead to less conservative time-dependent conditions, represented as a set of linear matrix inequalities (LMIs) that can be efficiently solved using the LMI or YALMIP toolboxes. In addition, the proposed observer includes the widely used proportional observer (PO) and proportional integral observer (PIO) as specific cases. Two examples are presented to demonstrate the validity and effectiveness of the results.

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一类具有时变延迟的 Lipschitz 非线性离散时间系统的 H∞ 动态观测器设计

本研究探讨具有时变延迟(TVD)和干扰的离散非线性系统(DTNLS)的H∞$$ {H}_{\infty } $$动态观测器(HDO)的发展。该方法是利用广义互凸矩阵不等式(GRCMI)以及基于jensen不等式(JBI)和基于WBI的wwinger不等式(WBI)构造具有双求和项的增广Lyapunov-Krasovskii函数(LKF)。这导致保守性较低的时间依赖条件，表示为一组线性矩阵不等式(LMI)，可以使用LMI或YALMIP工具箱有效地求解。此外，所提出的观测器还包括广泛使用的比例观测器(PO)和比例积分观测器(PIO)作为具体案例。通过两个算例验证了所得结果的正确性和有效性。

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Optimal Control Applications and Methods

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