具有无限马尔可夫二维Roesser系统的模糊H∞状态反馈控制

The fuzzy state feedback H∞ control of two-dimensional Roesser system with infinite Markov jumps

主要研究了带有无限状态空间马尔可夫链的二维Roesser Takagi-Sugeno(T-S)模糊模型系统的渐近均方稳定和H控制问题。首先,利用范数有界参数不确定性和转移概率矩阵,建立了离散时间无限马尔可夫链T-S模糊的Roesser模型系统;其次,通过构造一个李雅普诺夫函数,利用现代概率论和线性矩阵不等式等方法证明了闭环系统的渐近均方稳定性和H控制。最后,利用Matlab仿真模拟验证了其有效性和实用性。

This paper mainly studied the asymptotic mean square stable and the Hcontrol problem of a two-dimensional Roesser Takagi-Sugeno(T-S)fuzzy model system with an infinite Markov chain.First,this paper uses the bounded parameter uncertainty of the norm and the transition probability matrix to establish a discrete-time infinite Markov chain T-S fuzzy Roesser model system.Secondly,by constructing a Lyapunov function,modern probability theory and linear matrix inequality are used to prove the asymptotic mean square stability and Hcontrol of the closed-loop system.Finally,Matlab simulation is used to verify its effectiveness and practicability.