ABSTRACT

This note presents nested-saturation controllers for stabilising a class of feed-forward nonlinear systems that are subject to uncertain gains and an input delay. To verify the reduction of nested saturations, we adopt the strategy of partitioning the delay-interval, and can thus use the state values in a small domain to calculate a crucial composite term; when proving the asymptotic stability of the reduced time-delay system, we utilise the nested structure of saturations to make a coordinate transformation and consequently, can use a M-matrix based stability criterion. In this way, the analysis in two stages is straightforward, and a single group of parameter conditions are summarised to guarantee the global asymptotic stability of the closed-loop system.

摘要

本说明介绍了用于使一类前馈非线性系统稳定的嵌套饱和控制器，这些非线性系统会受到不确定的增益和输入延迟的影响。为了验证嵌套饱和度的降低，我们采用了对延迟间隔进行划分的策略，因此可以在较小的域中使用状态值来计算关键的合成项。在证明减少时滞系统的渐近稳定性时，我们利用饱和度的嵌套结构进行坐标转换，因此可以使用基于M矩阵的稳定性准则。这样，两个阶段的分析就很简单，并且汇总了一组参数条件以确保闭环系统的全局渐近稳定性。