Delay-dependent H∞ fuzzy observer-based control for discrete-time nonlinear systems with state delay

This paper studies the H∞ fuzzy observer-based control problem for discrete-time nonlinear systems with state delay via a fuzzy Lyapunov–Krasovskii functional (LKF) approach. The Takagi and Sugeno (T–S) fuzzy model is employed to represent a discrete-time nonlinear system with state delay. Based on a non-parallel distributed compensation (PDC) scheme, a new fuzzy LKF is first constructed to derive a delay-dependent condition such that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed level of H∞ disturbance attenuation. In the derivation process, two free fuzzy weighting matrices are introduced to express the relationship between the present state and delay state. Then, a novel linear matrix inequality (LMI) approach is proposed for the design of a delay-dependent H∞ fuzzy observer-based controller. The control and observer matrices can be solved directly by using the existing LMI optimization techniques. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.