LMI design approach to robust fuzzy sliding-mode observer in dynamical uncertain systems

This paper describes the dynamical uncertain systems by the Takagi-Sugeno (T-S) fuzzy dynamic model, and proposes a LMI design method of the robust fuzzy sliding mode observer by applying the robust sliding-mode observer design principle based on the singular value decomposition. Firstly, the Lyapunov function is used as the critical condition which ensures the consistent convergence of the designed observers and the asymptotic stability of states estimation, and then, the synthesis arithmetic of robust fuzzy sliding mode observer is designed by using LMI and pole placement approach, which the designed observer parameters are obtained by convex programming techniques for LMIs. Finally, numerical simulation results are presented to demonstrate the design fuzzy sliding mode observer for an inverted pendulum, and its stability is discussed under pole placements.