Improved Approach to Robust ${\cal H}_\infty$ Stabilization of Discrete-Time T–S Fuzzy Systems With Time-Varying Delays

This study is concerned with the robust stabilization problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. To improve the conditions for the solvability of the stabilization problem, a nonquadratic Lyapunov-Krasovskii functional with a triple-summation term is established, and a nonparallel distributed compensation (non-PDC) scheme is adopted along with the matrixtransformation technique. In addition, an appropriate free-weightingmatrix method is proposed to exploit novel slack variables for null sum terms, especially resulting from Σ
_i
(x
_i+1
- x
_i
)
^T
(·)(x
_i+1
+ x
_i
).