一类非线性时滞系统的采样控制

Sampled-data control for a class of nonlinear time-delay systems

针对于采样区间具有已知上界的非线性时滞系统,分别考虑了常采样和变采样两种情况下的采样控制问题.目标是设计一个状态反馈采样控制器,使得闭环系统指数稳定,并且满足给定的性能指标.基于输入延迟方法,可以将采样控制系统转化成具有时变延迟的连续系统.引入了新的时间依赖Lyapunov函数,这些Lyapunov函数在下一个采样时间到来之前没有增长.以线性矩阵不等式(LMI,Linear Matrix Inequality)的形式给出了具有时变延迟的非线性扰动系统指数稳定的充分条件.仿真结果说明了所提方法可以提高系统的抗扰能力.

The problem of sampled-data control was investigated for a class of nonlinear time-delay per- turbed systems, where the upper bound of sampling intervals was known and both constant sampling and varia- ble sampling were considered. The objective is to design a state-feedback sampled-data controller, which guar- antees the closed-loop system exponentially stable and satisfies given performance index. By applying an input delay approach, the sampled-data control system was transformed into a continuous time-delay system. The no- vel time-dependent Lyapunov functions were introduced, which did not grow before the arrival of the next sam- piing time. By linear matrix inequality（LMI） approach, sufficient conditions were obtained, under which the nonlinear time-delay perturbed systems were exponentially stable. And simulation results show that the pro- posed method can improve the immunity of system.