一类不确定的非线性时滞大系统的鲁棒稳定性

Robust stability of uncertain nonlinear large-scale systems with time-delay

针对具有分离变量的不确定时滞大规模系统,基于非线性的Lyapunov泛函和矩阵不等式的分析方法,获得了一些不依赖时滞的鲁棒稳定性判据。所考虑的不确定时滞大规模系统具有时变未知且有界的不确定参数和状态时滞,非线性的执行机构具有分离变量的形式。这类系统也可以看成线性系统的自然推广,其实际背景是把一个线性系统的部分线性元件换成了非线性元件。所获得的鲁棒稳定性判据适用于系统具有多个非线性执行机构的情形。

Based on the analysis method of a nonlinear Lyapunov function and a matrix inequality, some sufficient conditions with delay-independent are given for robust stability of a class of uncertain nonlinear large-scale systems with time-delay. The uncertain time-delay large-scale systems under consideration are described by state differential equation with time-varying unknown-but-bounded uncertain parameters and delayed state. The non-linearities have the form of separated variables, this kind of systems can be considered the generalization of a linear system, and its actual background simply is that a linear component is replaced by nonlinear one in the linear systems. These criteria of robust stability are applicable to the case of multiple non-linearities.