变周期采样系统指数稳定的新条件

发布时间：2018-06-21 14:58

本文选题：采样系统 + 指数稳定　；参考：《控制理论与应用》2016年10期

【摘要】：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.
[Abstract]:In this paper, the exponential stability of linear sampling systems with variable period sampling is studied. Based on the discrete time Lyapunov theory, a new Lyapunov-like functional is constructed. The functional is not only time-varying, but also increases the integral of the quadratic term of the state, and does not require a positive definite in the sampling interval. Using this new Lyapunov functional, the exponential stability theorem is proposed for a class of nonlinear sampling systems, and then the improved Wirtinger integral inequality is used. The conditions of linear matrix inequalities (LMIs) for exponential stability and asymptotic stability of linear sampling systems with variable periods are derived. Finally, an example is given to show that the results obtained are less conservative than those reported in some existing literatures.
【作者单位】：曲阜师范大学自动化研究所;
【基金】：国家自然科学基金项目(61374090) 山东省高等院校科研创新团队项目山东省泰山学者人才工程项目~~
【分类号】：TP13

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