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New stability and stabilization methods for nonlinear systems with time-varying delays

机译：具有时变时滞的非线性系统的新型稳定方法

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摘要

This paper establishes new robust delay-dependent stability and stabilization methods for a class of nominally linear continuous-time systems with time-varying delays. The parameter uncertainties are convex-bounded and the unknown nonlinearities are time-varying perturbations satisfying Lipschitz conditions in the state and delayed state. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics via descriptor format. Delay-dependent stability analysis is performed to characterize linear matrix inequalities (LMIs)-based conditions under which the nominally linear delay system is robustly asymptotically stable with a γ-level L_2-gain. Then we design delay-dependent feedback stabilization schemes: a static one based on state-measurements and a dynamic one based on observer-based output feedback. In both schemes, the closed-loop feedback system enjoys the delay-dependent asymptotic stability with a prescribed γ-level L_2-gain. The feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example.
机译：本文为一类具有时变时滞的名义线性连续时间系统建立了新的鲁棒时滞相关的稳定和镇定方法。参数不确定性是凸界的，未知非线性是时态扰动，满足状态和延迟状态下的Lipschitz条件。构建适当的Lyapunov函数，以通过描述符格式展现依赖于延迟的动力学。进行依赖于延迟的稳定性分析，以表征基于线性矩阵不等式（LMI）的条件，在该条件下，名义上的线性延迟系统具有γ级L_2增益，鲁棒渐近稳定。然后，我们设计了依赖于延迟的反馈稳定方案：基于状态测量的静态方案和基于观察者的输出反馈的动态方案。在这两种方案中，闭环反馈系统均具有规定的γ级L_2增益，具有与延迟有关的渐近稳定性。反馈增益由LMI上的凸优化确定。所有开发的结果均在一个具有代表性的示例上进行测试。

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