Observer-Based $H_{infty}$ Control for T–S Fuzzy Systems With Time Delay: Delay-Dependent Design Method

摘要

This correspondence studies the problem of observer-based $H_{infty}$ control for time-delay Takagi–Sugeno (T–S) fuzzy systems. It provides a delay-dependent linear matrix inequality (LMI)-based method for the control design. It is known that the key important problem in the literature, even for delay-independent case, lies in the difficulty of decoupling matrix variables in corresponding matrix inequalities. This correspondence suggests a decoupling technique for solving matrix inequalities with coupled variables, and provides an LMI-based algorithm by adopting the idea of the cone complementarity problem. The derivation relies on the appropriate choice of Lyaponuv–Krasovskii functionals which incorporate the intersections among local systems. Illustrative examples are given to show the effectiveness of the present delay-dependent result.