一类含输入和状态时滞的不确定非线性系统的鲁棒控制  

Robust Control for a Class of Uncertain Nonlinear Systems with Input and State Delays

作　　者：王坤[1] 朱作键[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《郑州大学学报（工学版）》2012年第6期27-31,共5页Journal of Zhengzhou University（Engineering Science）

基　　金：国家自然科学基金资助重点项目(60934003)

摘　　要：针对一类同时具有输入时滞、状态时滞和非线性扰动的不确定控制系统,研究了此类系统的鲁棒渐进稳定性和状态反馈控制律的设计两个问题.在矩阵分析理论和鲁棒稳定理论基础上,通过选择适当积分形式的Lyapunov函数,利用线性矩阵不等式(LMI)性质和Schur引理,推导出了此类时滞系统鲁棒渐近稳定的一个充分条件,并给出了一个保证此类系统鲁棒渐近稳定的状态反馈控制律.最后,针对此类系统,通过MATLAB中LMI工具箱进行了数值模拟,证明了此充分条件和控制律的可行和有效.The robust asymptotic stability problem and state feedback controller problem for a class of uncertain systems are considered in view of the fact that the system contains input delay,state delay and nonlinear perturbation.Based on matrix analysis theory and robust stability theory,a sufficient condition of robust asymptotic stability for the system is derived.And in this process,the proper integral form of Lyapunov function was chosen,the properties of the linear matrix inequality（LMI） and Schur lemma were used.Moreover,a corresponding state feedback controller for the system was given to ensure the robust asymptotic stability of such systems.Finally,the feasibility and efficiency of the sufficient condition and controller were verified by numerical simulation,which was conducted through the LMI toolbox in MATLAB.

关 键 词：输入时滞 状态时滞 非线性扰动 鲁棒控制 矩阵分析 线性矩阵不等式 充分条件 控制律 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]