Adaptive sliding mode control design for a class of uncertain singularly perturbed nonlinear systems

This paper addresses adaptive sliding mode control (ASMC) of uncertain singularly perturbed nonlinear (USPN) systems with guaranteed H control performance. First, we use Takagi-Sugeno (T-S) fuzzy model to construct the USPN systems. Then, the sliding surface can be determined via linear matrix inequality (LMI) design procedure. Second, we propose neural network (NN)-based ASMC design to stabilise the USPN systems. The proposed methods are based on the Lyapunov stability theorem. The adaptive law can reduce the effect of uncertainty. The proposed NN-based ASMC will stabilise the USPN systems for all E (0, E*]. Simulation result reveals that the proposed NN-based ASMC scheme has better convergence time compared with the fuzzy control scheme (Li, T.-H.S., & Lin, K.J. (2004). Stabilization of singularly perturbed fuzzy systems, IEEE Transactions on Fuzzy Systems, 12, 579-595.).