摘要
研究了具有2个独立马尔可夫(Markov)过程的时滞离散线性正系统(DDPLSwTIMPs)的有限时间l_(1)-增益滤波问题.首先,利用Markov化状态方法将原系统转化为增广时滞系统后,第二次使用增广系统方法消除系统中出现的时滞,得到易于分析的增广常微分系统;接着,采用线性协正李雅普诺夫(Lyapunov)函数和多重克罗内克(Kronecker)积方法,以线性规划(LP)形式建立了DDPLSwTIMPs时滞相关的l_(1)-增益滤波充分条件,使得滤波误差系统不仅随机有限时间有界,而且还具有给定的有限时间l_(1)-增益性能指标;最后,利用矩阵分析方法将l_(1)-增益滤波器的设计转化为求解基于LP的矩阵不等式.数值算例验证表明,针对DDPLSwTIMPs所提出的l_(1)-增益滤波设计方案具备可行性和有效性.
This paper studies a finite-time l_(1)-gain filtering problem for discrete-time delayed positive linear systems with two independent Markov processes(DDPLSwTIMPs).Firstly,the original system is transformed into an augmented time-delayed system by using the Markovianization state method,the time delay in the system is eliminated by applying the augmented system method again,resulting in an augmented ordinary differential system that is easy to analyze.Subsequently,by means of the linear copositive Lyapunov function and multiple Kronecker product method,a delay-dependent sufficient condition for l_(1)-gain filtering of DDPLSwTIMPs is established in the form of linear programming(LP).This condition ensures that the resulting filtering error system is not only stochastically finite-time boundedness but also satisfying the prescribed finite-time l_(1)-gain performance index.Moreover,by using matrix analysis approach,the design of l_(1)-gain filter is converted into matrix inequalities solving LP-based.Finally,a numerical example is provided to verify the feasibility and effectiveness of the proposed l_(1)-gain filtering design scheme for DDPLSwTIMPs.
作者
蒋海慧
杨军
施开波
罗金南
贾杨
JIANG Haihui;YANG Jun;SHI Kaibo;LUO Jinnan;JIA Yang(College of Electrical Engineering,Southwest Minzu University,Chengdu 610041,China;School of Electronic Information and Electrical Engineering,Chengdu University,Chengdu 610106,China)
出处
《成都大学学报(自然科学版)》
2025年第4期392-398,423,共8页
Journal of Chengdu University(Natural Science Edition)
基金
西南民族大学科研启动金资助项目(RQD2022024)
四川省科技厅科技计划项目(2024NSFSC1404)。
