This paper investigates sampling dependent stability for aperiodic sampled-data systems by employing a Lyapunov-like functional that is time-dependent, and not imposed to be definite positive. Based on the system information on the sampling interval wholly rather than partly, a new Lyapunov-like functional is constructed, which extends existing ones by introducing the integral of the system state and the cross terms among this integral and the sampled state. To take advantage of the integral of the system state, integral equations of the sampled-data system are explored when estimating the derivative of the extended functional. By the Lyapunov-like functional theory, a new sampling dependent stability result is obtained for sampled-data systems without uncertainties. Then, the stability result is applied to sampled-data systems with polytopic uncertainties and a robust stability result is derived. At last, numerical examples are given to illustrate that the stability results improve over some existing ones.

本文研究了非周期采样数据系统的采样依赖稳定性，方法是采用与时间有关的Lyapunov样函数，并且不强求肯定。基于全部而非部分采样间隔上的系统信息，构造了一个新的Lyapunov类函数，该函数通过引入系统状态的积分以及该积分和采样状态之间的交叉项来扩展现有函数。为了利用系统状态的积分，在估计扩展函数的导数时，探索了采样数据系统的积分方程。通过类Lyapunov函数理论，可以得到没有不确定性的采样数据系统新的依赖采样的稳定性结果。然后，将稳定性结果应用于具有多主题不确定性的采样数据系统，并得出鲁棒的稳定性结果。最后，通过数值算例说明了稳定性结果比已有的改进方法。