title: Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control.
abstract: 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.
authors.affiliation: School of Automation Science and Electrical Engineering, Beihang University (Beijing University of Aeronautics and Astronautics), Beijing 100083, China. huainingwu@163.com
authors.forename: Huai-Ning
authors.initials: HN
authors.lastname: Wu
authors.forename: Kai-Yuan
authors.initials: KY
authors.lastname: Cai
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D017143:Fuzzy Logic; D008390:Markov Chains; D015233:Models, Statistical; D017711:Nonlinear Dynamics