Robust H∞ Control for Uncertain Type-2 Fuzzy Singular Systems with Input and State Delays

This paper investigates the robust H-infinity controller design for a class of nonlinear singular time-delay systems. The parametric uncertainties are also considered in this work. To solve the problem, firstly, the nonlinear system is modeled by using the interval type-2 T-S fuzzy theory. To analyze the stability, by choosing a proper Lyapunov functional, the delay-dependent characteristics are taken into account. Moreover, free weighting matrices are introduced to reduce the conservativeness. Consequently, using the linear matrix inequality technique, a sufficient condition for the stability of singular delayed control system is obtained. As to the controller design, this work introduces the concept of duality. Along with the stability condition, the desired robust H-infinity controller design can be derived. Finally, a numerical example is simulated and analyzed by using the Matlab LMI toolbox. According to the simulation results, the designed controller stabilizes the nonlinear systems and achieves the H-infinity performance. It verifies the correctness of the proposed controller design method.