带有非线性扰动的时变时滞系统的稳定性准则
Stability criteria for time-varying delay systems with nonlinear perturbations

研究了带有非线性扰动的时变时滞系统的稳定性问题. 基于时滞分割方法, 提出了保守性更小的系统稳定性分析准则. 利用一个自由参数将时滞区间分割为2个子区间, 进而构造了含有时滞分割点状态信息和3重积分项的Lyapunov-Krasovskii泛函, 并采用自由矩阵积分不等式界定泛函导数中的交叉项. 基于Lyapunov稳定性定理,得到了以线性矩阵不等式描述的时滞相关型稳定性准则. 数值算例表明该稳定性准则能够得到更大的时滞上界, 与已有结果相比具有更小的保守性.
The stability problem of systems with time-varying delay and nonlinear perturbations is reseached. Based on delay decomposition approach, a less conservative stability criterion is proposed. The delay interval is divided into two subintervals by a free parameter. Then, an appropriate Lyapunov-Krasovskii functional(LKF) containing state information of the partition point and some triple-integral terms is constructed. Cross-terms in the time derivative of LKF is dealt with free-matrix integral inequality. According to Lyapunov stability theory, a delay-dependent stability criteria in the framework of linear matrix inequality(LMI) is obtained. Numerical examples demonstrate that the proposed stability criteria can achieve larger upper bounds and has less conservatism than existing results.