Complex performance control using sliding mode fuzzy approach for discrete-time nonlinear systems via T-S fuzzy model with bilinear consequent part

In this paper, a stabilization problem for the discrete nonlinear system with external disturbance, multiplicative noises and multiple constraints has been discussed in accordance with the definition of Lyapunov stability. Based on fuzzy modeling approach, the overall fuzzy model of a nonlinear plant is transformed into a class of linear systems. Applying a Sliding Mode Fuzzy Control (SMFC) scheme, the designed controller causes the closed-loop system converging to the sliding surface and achieving the required control performance. For the control performance, the concepts of stability, individual state variance and passivity constraints are introduced for the sliding mode fuzzy control system. To apply convex optimal programming algorithm, some sufficient conditions derived in this paper are reduced to Linear Matrix Inequality (LMI) problem. At last, two simulation examples are proposed to demonstrate the applicability and usefulness of the proposed design method. One of the examples is to discuss the conservatism of this paper. Another is to show that the discrete truck-trailer system controlled by sliding mode fuzzy controller can achieve stability constraints, individual state variance constraints and passivity constraints.