This paper is focusing on the stability analysis of aperiodic sampled-data systems. The augmented Lyapunov functional is powerful to produce a stability criterion with less conservatism owing to the well construction of coupled relationships among time-dependent states. In this paper, a novel augmented Lyapunov functional involving the time-squared-dependent augmented term is presented under the double-side looped-functional technique, which considers coupled relationships more fully than the current ones. Then, an improved negative definiteness lemma based on adjustable parameters is developed, resulting in a less conservative negative definite condition for the derivative of the Lyapunov functional. Finally, a stability criterion is derived based on the Lyapunov functional and the improved lemma, whose effectiveness is illustrated with four numerical examples and one practical example.

本文的重点是非周期性采样数据系统的稳定性分析。由于时间依赖状态之间的耦合关系的良好构造，增强的Lyapunov函数强大地产生了具有较少保守性的稳定性判据。本文在双面循环函数技术的基础上，提出了一种新的扩展的Lyapunov泛函，涉及与时间平方相关的增强项，该函数比当前的耦合泛函更充分地考虑了耦合关系。然后，开发了一种基于可调整参数的改进的负定性引理，从而为Lyapunov泛函的导数带来了较不保守的负定条件。最后，根据Lyapunov泛函和改进的引理推导出稳定性判据，