Output-Feedback Control for T–S Fuzzy Delta Operator Systems With Time-Varying Delays via an Input–Output Approach

In this paper, the problem of induced $L_{2}$ disturbance attenuation control is investigated for discrete-time Takagi–Sugeno (T–S) fuzzy delta operator systems with time-varying delays and disturbance input via an input–output approach. A model transformation method is utilized to approximate the time-varying delay in T–S fuzzy delta operator systems. By applying the scaled small gain (SSG) theorem and Lyapunov–Krasovskii functional approach, a sufficient condition is established to guarantee that the closed-loop system is asymptotically stable and has an induced $L_{2}$ disturbance attenuation performance. The existence condition of the dynamic output-feedback controller can be solved via convex optimization problems. Finally, simulation results are given to demonstrate the feasibility and effectiveness of the proposed method.