Wu Huai-Ning, Cai Kai-Yuan
School of Automation Science and Electrical Engineering, Beihang University (Beijing University of Aeronautics and Astronautics), Beijing 100083, China.
IEEE Trans Syst Man Cybern B Cybern. 2006 Jun;36(3):509-19. doi: 10.1109/tsmcb.2005.862486.
This paper is concerned with the robust-stabilization problem of uncertain Markovian jump nonlinear systems (MJNSs) without mode observations via a fuzzy-control approach. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. The aim is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system (MJFS) is robustly stochastically stable. Based on a stochastic Lyapunov function, a robust-stabilization condition using a mode-independent fuzzy controller is derived for the uncertain MJFS in terms of linear matrix inequalities (LMIs). A new improved LMI formulation is used to alleviate the interrelation between the stochastic Lyapunov matrix and the system matrices containing controller variables in the derivation process. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.
本文通过模糊控制方法研究了无模式观测的不确定马尔可夫跳跃非线性系统（MJNSs）的鲁棒镇定问题。采用高木和菅野（T-S）模糊模型来表示具有范数有界参数不确定性和马尔可夫跳跃参数的非线性系统。目的是设计一个与模式无关的模糊控制器，使得闭环马尔可夫跳跃模糊系统（MJFS）鲁棒随机稳定。基于一个随机李雅普诺夫函数，针对不确定MJFS，通过线性矩阵不等式（LMI）推导了使用与模式无关的模糊控制器的鲁棒镇定条件。在推导过程中，采用了一种新的改进LMI公式来减轻随机李雅普诺夫矩阵与包含控制器变量的系统矩阵之间的相互关系。最后，给出了一个仿真例子来说明所提出设计方法的有效性。
