H ∞ Control Based on Partitioning the Range of Fuzzy Weights for Uncertain Discrete-Time T-S Fuzzy Systems

This paper proposes a new non-parallel distributed compensation (non-PDC) scheme of $H_{\infty}$ control for uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems. To utilizing the partition to the range of the fuzzy weights, the proposed scheme sets the variables to be second-order parametric in both the current- and past-time fuzzy weights, which results in a third-order parameterized condition. Then, the scheme uses the elimination lemma, where a decision variable is designed to be constant piecewise by partitioning the range of the parameters, so that the resulting condition is first-order parameterized. Consequently, the switching controller is developed by utilizing the extreme points of each partition. Numerical examples are provided to illustrate the effectiveness of the proposed approach.