一类非线性时滞系统的保性能控制器设计  

Guaranteed Cost Controller Design for a Class of Nonlinear Time-Delay System

作　　者：王天成[1] 王燕[1] 

机构地区：[1]鲁东大学数学与信息学院,山东烟台264025

出　　处：《控制工程》2011年第5期707-709,共3页Control Engineering of China

基　　金：国家自然科学基金资助项目(107711226;0774016)

摘　　要：针对一类具有非线性控制输入的参数不确定时滞系统和给定的保性能指标,研究了此类系统的保性能控制问题。利用Lyapunov稳定性定理和线性矩阵不等式工具,得到了非线性不确定时滞系统的保性能控制存在的充分条件。与现有结果相比,考虑的保性能控制器是非线性的,并且保性能控制器可由线性矩阵不等式的解给出。得到的保性能控制器不仅保证闭环系统的局部渐近稳定性而且能够使得系统满足一定的性能指标。进一步,建立一个具有线性矩阵不等式约束的凸优化问题,从而可以借助Matlab软件中的线性矩阵不等式工具箱求解,基于相应的线性矩阵不等式的可行解,给出非线性不确定时滞系统的保性能控制律的构造方法。最后的仿真实例表明了其可行性。The guaranteed cost control problem for a class of uncertain nonlinear control input systems with time-delay and a prescribedperformance index is discussed. By means of Lyapunov stability theory and linear matrix inequalities （ LMIs）, a sufficient condition for the existence of nonlinear guaranteed cost controller for a kind of uncertain system with time-delay is derived. Compared with the existing results, the guaranteed cost controller is nonlinear and the nonlinear guaranteed cost control law of system is presented in terms of the solutions of LMIs. The obtained controller not only guarantees that the closed-loop system is local asymptotic stability but also satisfies a prescribed performance index. Furthermore, a convex optimization problem constrained with LMIs is formulated, the solutions can be efficiently solved by means of Matlab LMI toolbox. Based on the solutions of LMIs, the nonlinear guaranteed controller is presented. Finally, an illustrative example demonstrates the effectiveness of the proposed method.

关 键 词：保性能控制 LYAPUNOV泛函 时滞 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]