A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays

Abstract

This paper focuses on analyzing a new model transformation of discrete-time Takagi–Sugeno (T–S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new comparison model is proposed by employing a new approximation for time-varying delay state, and then, a delay partitioning method is used to analyze the scaled small gain of this comparison model. A sufficient condition on discrete-time T–S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\ell_{2}$</tex></formula> disturbance attenuation performance, is derived by employing the scaled small-gain theorem. Then, the solvability condition for the induced <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\ell_{2}$</tex></formula> DOF control is also established, by which the DOF controller can be solved as linear matrix inequality optimization problems. Finally, examples are provided to illustrate the effectiveness of the proposed approaches.