不确定广义双线性系统的鲁棒镇定

Robust Stabilization for Singular Bilinear Systems with Uncertainty

针对带有不确定参数的广义双线性系统的鲁棒镇定问题进行研究,其中不确定参数是时变且范数有界的.本文的目的是设计状态反馈控制器,使得对所有满足条件的不确定参数闭环系统都是渐近稳定的.通过引入广义二次稳定的概念、采用Lyapunov方法,分别给出了不确定广义双线性系统在两种不同情形下可镇定的充分条件;此外,两个数值例子分别说明了两种设计方法的有效性和合理性.

The problem of robust stabilization for uncertain singular bilinear systems （SBS） with norm-bounded timevarying uncertainties is studied. The purpose of this paper is to design a state feedback controller such that the closed-loop system is asymptotically stable for all admissible uncertainties. The sufficient conditions of stabilization for SBS with uncertainties in two different conditions are presented respectively via the notion of generated quadratic stability and Lyapunov method. Furthermore, effectiveness and rationality of the two design methods are illustrated by two numerical examples respectively.