Linearization of discrete-time T-S fuzzy model with multiple input

Abstract

Linearization of T-S fuzzy model is difficult to be achieved by using existing linearization methods because fuzzy rules and membership functions are included in T-S fuzzy models. In this paper, a new linearization method is proposed for discrete time T-S fuzzy system based on the properties of T-S fuzzy theorem. The local linear models of a T-S fuzzy model are transformed to a controllable canonical form respectively, and their T-S fuzzy combination results in a feedback linearizable T-S fuzzy model. Based on this model, a nonlinear state feedback linearizing input is determined. Nonlinear states transformation is inferred from the linear state transformations for the controllable canonical form. The proposed method is more intuitive and easier to understand mathematically compared to the well-known feedback linearization technique which requires a profound mathematical background. The feedback linearizable condition of this paper is also weakened compared to the conventional feedback linearization.