中文摘要：

提供了分析多边形不确定性周期采样系统鲁棒指数稳定性的新方法．首先，对确定性采样系统，构造了一个类Lyapunov泛函．该泛函引入了状态积分项而放松了对通常意义下Lyapunov泛函必须正定的要求．利用该泛函以及给出的关于线性采样系统指数稳定的新引理，结合改进的Wirtinger积分不等式，导出了采样依赖指数稳定性准则．然后，该准则被推广到多边形不确定性周期采样系统，得到了鲁棒采样依赖指数稳定性准则．最后，举例说明了所得稳定性结果比现存的某些文献报道的结果保守性较小．

英文摘要：

This paper provides a new approach to robust exponential stability for sampled-data systems with ploytopic uncertainty under periodic sampling. Firstly, a new Lyapunov-like functional is constructed, which contains an integral quadratic term of the states and is not necessarily positive definite compared with a Lyapunov functional in general. Employing this new Lyapunov functional and a lemma proposed in this paper to study the exponential stability for sampled-data systems under periodic sampling, a new sampling-interval-dependent exponential stability criterion is derived by taking advantages of the improved Wirtinger inequality. Then this criterion is extended to sampled-data systems with polytopic uncertainty, and a robust sampling-interval-dependent exponential stability criterion is obtained. Finally, examples are given to illustrate that the stability criteria have less conservatism compared with some existing ones.