变周期采样系统指数稳定的新条件
New conditions for exponential stability of sampled-data systems under aperiodic sampling

本文研究了线性采样系统在变周期采样下的指数稳定性问题. 基于离散时间Lyapunov理论, 构造了一个新 的类Lyapunov泛函. 该泛函不仅是时变的, 还增加了对状态二次项的积分, 而且不要求在采样区间内正定. 利用这 一新的类Lyapunov泛函, 本文首先针对一类非线性采样系统提出了指数稳定性定理, 再结合改进的Wirtinger积分不 等式, 导出了使变周期线性采样系统指数稳定以及渐近稳定的线性矩阵不等式条件. 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.
This article is concerned with the exponential stability problem of linear sampled-data systems under aperiodic sampling. Based on discrete-time Lyapunov theorem, a new Lyaponov-like functional is constructed with the following features. It explicitly depends on time t, contains the integral quadratic term of the states, and is not required to be positive definite between sampling instants. Based on this new Lyapunov-like functional, a new theorem is proposed in this paper to study the exponential stability of a class of nonlinear sampled-data systems firstly. And then new conditions for the linear sampled-data systems under aperiodic sampling to be exponentially and asymptotically stable are given respectively in terms of linear matrix inequalities by taking advantages of the new theorem and the improvedWirtinger integral inequality. Examples are provided to illustrate that the stability conditions have less conservatism compared with some existing ones.