A design of discrete-time SMC for nonlinear systems based on fuzzy T-S model

An innovated investigation of the control problem for nonlinear discrete-time plant systems via Takagi-Sugeno fuzzy model was carried out. Firstly, nonlinear dynamic plants are represented by such a fuzzy model, and then the overall fuzzy model of nonlinear plant is transformed into a class of uncertain linear systems. Thus the stabilization problem of nonlinear plants was mapped into equivalent robust stabilization problem of uncertain linear systems with mismatched uncertainties. The robust stabilization of such uncertain systems is achieved by applying discrete-time sliding mode control approach. The stable sliding surface is designed via linear matrix inequalities to reduce the influence of mismatched uncertainties while also a sufficient condition for its existence was derived too. The synthesis design of the SMC guarantees system robust stabilization in closed loop. Chattering around the sliding surface in sliding mode control is also considerably reduced by this design. This novel technique was applied to the trailer-truck benchmark example and the essential simulation results are given to demonstrate feasibility and performance effectiveness of the proposed method.