Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control

作者：Wu Huai Ning^*; Cai Kai Yuan

来源：IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics , 2006, 36(3): 509-519.

DOI：10.1109/TSMCB.2005.862486

• fuzzy control
• linear matrix inequality (LMI)
• Markovian jump parameters
• robust control
• stochastic stability
• uncertain nonlinear systems

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.

• 出版日期2006-6
• 单位北京航空航天大学