非线性广义Markov跳变系统的异步耗散控制  

Asynchronous Dissipative Control for Nonlinear Generalized Markov Jump Systems

作　　者：杨冬梅[1] 李达 YANG Dong-mei;LI Da(School of Sciences,Northeastern University,Shenyang 110819,China)

机构地区：[1]东北大学理学院,辽宁沈阳110819

出　　处：《东北大学学报（自然科学版）》2021年第9期1226-1230,共5页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(61673100).

摘　　要：研究了一类在Takagi-Sugeno模糊规则下的连续时间非线性广义Markov跳变系统的严格异步耗散控制问题.首先,通过构造保守性较小的模态独立Lyapunov函数,推广到相应的广义系统并给出随机稳定且严格耗散的充分条件.然后,引入在实际中应用广泛的隐Markov模型,通过将状态转移概率与隐Markov模型的相关的条件概率相结合,并通过Schur变换,设计了可以与原系统异步运行的模糊状态反馈控制器,以保证闭环系统的随机稳定和严格耗散.最后,数值仿真使用Matlab中线性矩阵不等式(LMI)的工具箱来验证,说明结论的有效性.The problem of strictly asynchronous dissipative control for a class of continuous time nonlinear generalized Markov jump systems under Takagi-Sugeno fuzzy rules is studied.Firstly,by constructing a less conservative mode independent Lyapunov function,the sufficient conditions for stochastic stability and strict dissipation of generalized system are discussed.Then,the hidden Markov model that is widely used in practice is introduced.By combining the state transition probability with the conditional probability of the hidden Markov process,and through Schur transformation,a fuzzy state feedback controller is designed,which can operate asynchronously with the original system,so as to ensure the stochastic stability and strict dissipation of the closed-loop system.Finally,numerical simulation using Matlab linear matrix inequality(LMI)toolbox is applied to verify the effectiveness of the conclusion.

关 键 词：异步控制 模糊规则 广义Markov跳变系统 严格耗散 随机稳定 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]