Induced ℓ2 control of discrete-time Takagi-Sugeno fuzzy systems with time-varying delays via dynamic output feedback

This paper is concerned with analyzing a novel 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 auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary 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 ℓ
₂
disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the solvability condition for the induced ℓ
₂
DOF control is also established, by which the DOF controller can be found by solving a set of linear matrix inequalities (LMIs).