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

Abstract

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 ℓ2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the solvability condition for the induced ℓ2 DOF control is also established, by which the DOF controller can be found by solving a set of linear matrix inequalities (LMIs).