2-D离散时滞系统的新时滞相关稳定性准则  

New delay-variation-dependent stability criterion for 2-D discrete systems with delays

作　　者：彭丹[1] 张明霞 Peng Dan;Zhang Mingxia(School of Science,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《河南师范大学学报（自然科学版）》2024年第3期50-61,共12页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金杰出青年科学基金(61825304);河北省自然科学基金(F2022203085);河北省省级科技计划资助(F2020203037);河北省自然科学基金创新研究群体项目(F2020203013).

摘　　要：研究了具有时变时滞的二维(two-dimensional,2-D)离散系统的时滞相关稳定性问题.所创建的Lyapunov-Krasovskii泛函(Lyapunov-Krasovskii functionals,LKFs)考虑在二次项和单项求和项中引入时滞相关矩阵,包含了更多的状态信息.同时在单项求和项中引入增广向量矩阵,并给出适用于2-D系统的多重辅助函数不等式和互凸组合不等式,用于处理LKFs差分,以便降低计算负担.然后,为具有时变时滞的2-D离散系统推导出保守性更小的稳定性准则.通过两个数值算例验证了所设计方法的有效性和优越性.The delay-variation-dependent stability problem for two-dimensional(2-D)discrete-time systems with delays is studied.The Lyapunov-Krasovskii functionals(LKFs)are constructed by using delay-dependent matrices in the quadratic and single-sum terms,respectively,considering more state information.It is also the first time that the augmented vector matrices in the single summation term have been studied the system stability.Meanwhile,the multiple auxiliary function inequality and reciprocally convex inequality suitable for 2-D systems are given to process LKFs differentiation so as to reduce the computational burden.Derive a less conservative stability criterion for 2-D discrete systems with time-varying delays.The effectiveness and superiority of the devised method is confirmed by two numerical examples.

关 键 词：二维离散系统 时变时滞 LYAPUNOV-KRASOVSKII泛函 多重辅助函数不等式 互凸组合不等式 

分 类 号：O231[理学—运筹学与控制论]