一类线性不确定定常时滞系统的鲁棒镇定

Robust stabilization for linear uncertain time-delay systems with nonlinear perturbation

研究了一类带有非线性扰动的线性不确定时滞系统的鲁棒镇定问题。在闭环系统的稳定性结果基础上,给出了时滞系统的鲁棒控制策略,推导出控制律存在的一个充分条件,该条件被进一步等价地转化为一个线性矩阵不等式的可解性问题。根据Lyapunov稳定性原理所设计的控制器确保了闭环系统渐近稳定。最后,通过数值例子说明了此方法的正确性与有效性。

The problem of robust stabilization for linear uncertain time delay systems with nonlinear perturbation is reviewed. Based on Lyapunov stability theory,the delay dependent stabilization criteria for the system is developed. Robust controller is given by analyzing the stability of closed-loop system. The sufficient condition for the existence of controller is deduced. Then, the condition is further equivalent to the solvability of certain linear matrix inequality （LMI）. Robust controller is given to guarantee stability of closed-loop system. Finally,an example is employed to illustrate the validity and effectiveness of the pro- posed method.