Zhang Hongbin, Feng Gang
Center for Nonlinear and Complex Systems, Schoolof Electronic Engineering, University of Electronic Science and Technology ofChina, Chengdu 610054, China.
IEEE Trans Syst Man Cybern B Cybern. 2008 Oct;38(5):1390-401. doi: 10.1109/TSMCB.2008.927267.
This paper is concerned with stability analysis and H(infinity) decentralized control of discrete-time fuzzy large-scale systems based on piecewise Lyapunov functions. The fuzzy large-scale systems consist of J interconnected discrete-time Takagi-Sugeno (T-S) fuzzy subsystems, and the stability analysis is based on Lyapunov functions that are piecewise quadratic. It is shown that the stability of the discrete-time fuzzy large-scale systems can be established if a piecewise quadratic Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. The H(infinity) controllers are also designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions. It is demonstrated via numerical examples that the stability and controller synthesis results based on the piecewise quadratic Lyapunov functions are less conservative than those based on the common quadratic Lyapunov functions.
本文研究基于分段李雅普诺夫函数的离散时间模糊大系统的稳定性分析和H∞分散控制。模糊大系统由J个相互连接的离散时间高木-关野（T-S）模糊子系统组成，稳定性分析基于分段二次李雅普诺夫函数。结果表明，如果能够构造分段二次李雅普诺夫函数，则可以建立离散时间模糊大系统的稳定性，并且该函数可以通过求解一组数值上可行的线性矩阵不等式（LMI）得到。基于这些强大的分段二次李雅普诺夫函数，通过求解一组LMI来设计H∞控制器。数值算例表明，基于分段二次李雅普诺夫函数的稳定性和控制器综合结果比基于普通二次李雅普诺夫函数的结果保守性更低。
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