多时滞非线性Lurie控制系统时滞相关绝对稳定性

为了研究具有非线性干扰项的多时滞Lurie控制系统的稳定性问题,依据Lyapunov稳定性理论,利用线性矩阵不等式方法,通过一个改进的新积分不等式,给出了一个新的判断系统稳定的新方法--积分不等式法.该方法不必进行模型变换和交叉项的确定,是判断Lurie系统时滞相关绝对稳定的充分条件,并以线性矩阵不等式的形式给出.相应的结果可推广到不确定的系统和间接系统.几个实例证明与现有文献结果相比,具有较小的保守性.

Delay-dependent absolute stability of nonlinear Lurie control systems with multiple time-delays

The stability of Lurie type control systems with multiple time-delays and nonlinearities is considered. Based on the Lyapunov stability theory , using an improved new integral inequality and the method of linear matrix inequality, a refined method called the integral inequality approach is presented. Neither model transformation nor bounding technique for cross terms is involved, and a sufficient condition for the absolute stability of Lurie system is derived and expressed in the form of linear matrix inequality. The criterion is also extended to systems with uncertainties and indirection. Examples are given to illustrate that the proposed criteria are less conservative than other existing ones.