Stability analysis of time-varying systems via parameter-dependent homogeneous Lyapunov functions  

基于参数依赖齐次多项式的时变系统稳定性分析(英文)

作　　者：张化生[1,2,3] 张侃健[1,2] 

机构地区：[1]东南大学复杂工程系统测量与控制教育部重点实验室,南京210096 [2]东南大学自动化学院,南京210096 [3]聊城大学数学科学学院,聊城252000

出　　处：《Journal of Southeast University(English Edition)》2014年第3期302-305,共4页东南大学学报（英文版）

基　　金：The Major Program of National Natural Science Foundation of China(No.11190015);the National Natural Science Foundation of China(No.61374006)

摘　　要：This paper considers the stability analysis of linear continuous-time systems, and that the dynamic matrices are affected by uncertain time-varying parameters, which are assumed to be bounded, continuously differentiable, with bounded rates of variation. First, sufficient conditions of stability for time-varying systems are given by the commonly used parameter-dependent quadratic Lyapunov function. Moreover, the use of homogeneous polynomial Lyapunov functions for the stability analysis of the linear system subject to the time-varying parametric uncertainty is introduced. Sufficient conditions to determine the sought after Lyapunov function is derived via a suitable paramenterization of polynomial homogeneous forms. A numerical example is given to illustrate that the stability conditions are less conservative than similar tests in the literature.基于齐次多项式Lyapunov函数这一新工具研究了时变不确定系统鲁棒稳定性问题.针对常见的含参数时变且有界连续可微线性系统的最大稳定区域问题,首先构造常用的参数依赖二次Lyapunov函数,进而给出一个时变系统稳定的充分条件.然后,通过构造适合的参数依赖齐次Lyapunov函数,并利用齐次多项式矩阵表示方法,最终以线性不等式的形式给出系统全局渐近稳定的一个充分条件.数值仿真结果表明齐次Lyapunov函数方法得到的结论对于某些系统比之前类似文献具有更小的保守性.

关 键 词：linear time-varying systems polytopic uncertainty robust stability linear matrix inequality 

分 类 号：TP202.1[自动化与计算机技术—检测技术与自动化装置] TP271.7[自动化与计算机技术—控制科学与工程]