不确定性Lurie控制系统鲁棒绝对稳定性的LMI方法

LMI approach for robust stability of Lurie control systems with uncertainties

对于具有时变结构不确定性Lurie控制系统,给出了关于Lurie型Lyapunov函数中正定矩阵和积分项系数的线性矩阵不等式,讨论了无穷扇形角的情形和有限扇形角的情形.研究结果表明:通过线性矩阵不等式的解构造的Lyapunov函数来保证系统的鲁棒绝对稳定性,不必选择和调整参数;所获得的结果适用于系统具有多个非线性执行机构的情形,克服了图解法检验频率的困难.

Popov frequency domain criterion for robust stability of Lurie control systems with multiple non-linearities will encounter difficulty since it can not be tested by illustration. On the other hand, when the Lurie-type Lyapunov function is adopted to determine the robust stability, it is difficult to find suitable positive definite matrix and coefficients of the integral items of the Lyapunov function to guarantee the robust stability. The parameters in the existing papers need to be readjusted again and again. In this paper, a LMI for the positive definite matrix and the coefficients of the integral items of the Lurie-type Lyapunov function for Lurie control systems with time-varying uncertainties is given. The Lyapunov function constructed by the solution of the LMI is adopted to guarantee the robust stability of the systems, and the parameters don't need to be readjusted. Not only the case of the finite sector but also the infinite sector are discussed, and the conclusion is applicable to the case of multiple non-linearities. Finally, an example is provided to demonstrate the effectiveness of the proposed method, and the relationship between the size of the sector and the robustness is analyzed through the example.