Sliding Mode Control of a Class of Uncertain Nonlinear Time-Delay Systems Using LMI and TS Recurrent Fuzzy Neural Network

This paper proposes the sliding mode control using LMI techniques and adaptive recurrent fuzzy neural network (RFNN) for a class of uncertain nonlinear time-delay systems. First, a novel TS recurrent fuzzy neural network (TS-RFNN) is developed to provide more flexible and powerful compensation of system uncertainty. Then, the TS-RFNN based sliding model control is proposed for uncertain time-delay systems. In detail, sliding surface design is derived to cope with the non-Isidori-Bynes canonical form of dynamics, unknown delay time, and mismatched uncertainties. Based on the Lyapunov-Krasoviskii method, the asymptotic stability condition of the sliding motion is formulated into solving a Linear Matrix Inequality (LMI) problem which is independent on the time-varying delay. Furthermore, the input coupling uncertainty is also taken into our consideration. The overall controlled system achieves asymptotic stability even if considering poor modeling. The contributions include: i) asymptotic sliding surface is designed from solving a simple and legible delay-independent LMI; and ii) the TS-RFNN is more realizable (due to fewer fuzzy rules being used). Finally, simulation results demonstrate the validity of the proposed control scheme.