研究了变周期采样系统的采样区间依赖稳定性问题. 采用类Lyapunov泛函方法研究采样系统的稳定性与采样区间的关系, 该类Lyapunov泛函不强求正定也不要求连续. 通过增加状态与状态导数的交叉项推广了类Lyapunov泛函, 然后用新的不等式处理该类Lyapunov泛函的导数, 基于类Lyapunov泛函方法导出了采样区间依赖稳定性新结果, 然后, 在凸多胞型不确定采样系统中推广该结果, 得到了鲁棒采样渐近稳定性新准则. 最后, 用3个仿真例子说明了文章结果比现有的某些结果保守性小.

This paper is concerned with the sampling-interval-dependent stability of sampled-data systems under aperiodic sampling. It adopts Lyapunov-like functional method to investigate the relationship between the stability of sampled-data systems and the sampling-interval. The Lyapunov-like functional is not necessarily positive definite nor continuous. A new Lyapunov-like functional is constructed, which contains the cross term of the state and its derivative. Then by taking advantage of a new inequality to deal with the Lyapunov-like functional derivative, based on the Lyapunov-like functional method, a new result is obtained about the sampling-interval-dependent stability. The result is extended to sampled-data systems under aperiodic sampling with polytopic uncertainty, and a new criterion is derived about the robust stability of the uncertain system. Lastly, three examples show that the proposed results have less conservatism than some existing ones.