Model Reduction of Discrete-Time Interval Type-2 T–S Fuzzy Systems

This paper addresses the model reduction problem of discrete-time interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy systems, which represent the discrete-time nonlinear systems subject to uncertainty. With the use of IT2 fuzzy sets, the uncertainty of the discrete-time nonlinear system can be captured by the lower and upper membership functions. For a given high-order discrete-time IT2 T–S fuzzy system, the purpose is to find a lower dimensional system to approximate the original system. To achieve the approximation performance, an
$\mathcal {H}_\infty$
norm is used to suppress the error between the original system and its simplified system. By introducing a membership-functions-dependent technique and applying a convex linearization method, a membership-functions-dependent condition, which takes the information of membership functions into account, is obtained to reduce the dimensions of system matrices and the number of fuzzy rules of the system. All the obtained theorems are represented as in the form of linear matrix inequalities. Finally, simulation results are demonstrated to show the effectiveness of the derived results.