障碍函数法在状态约束混杂系统稳定性中的应用  

Application of Barrier Function Method to Stability of State Constrained Hybrid Systems

作　　者：李亮亮 姜文琳 LI Liangliang;JIANG Wenlin(School of Mathematical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2022年第4期13-17,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省自然科学基金项目(2108085QA08);安徽省高校自然科学重点项目(KJ2021A0529)。

摘　　要：文章采用障碍Lyapunov函数法考虑状态约束脉冲非线性系统的稳定性及控制问题.通过构造一类障碍Lyapunov函数,利用辅助矩阵、数学归纳等方法,给出状态约束混杂微分系统稳定的充分条件,同时能够利用所提出的方法研究状态反馈输入控制下状态约束脉冲动力网络系统的镇定问题.In this paper,the stability and control problems of state constrained nonlinear impulsive systems are considered by the barrier Lyapunov function method.By constructing a class of symmetric barrier Lyapu⁃nov functions,and introducing the auxiliary matrix and inductive method,the sufficient conditions for the sta⁃bility of hybrid differential systems with state constraints are given.At the same time,the proposed method can be used to study the stabilization of state constrained impulsive dynamic network systems under the state feedback input control.

关 键 词：状态约束 脉冲系统 障碍函数 非线性系统 稳定性 

分 类 号：O193[理学—数学]