Fuzzy hyperbolic H∞ filter design for a class of nonlinear discrete-time dynamic systems

This paper studies fuzzy hyperbolic H_∞ filter for signal estimation of nonlinear discrete-time systems with state time delay. The fuzzy hyperbolic model (FHM) can be used to establish models for certain unknown complex systems. Furthermore, the main advantage of using the FHM over the Takagi-Sugeno fuzzy model are that no premise structure identification is needed and no completeness design of premise variables space is needed. Also an FHM is a kind of valid global description and nonlinear model in nature. First, FHM is proposed to represent the state-space model for nonlinear discrete-time systems. Next, we design a stable fuzzy H_∞ filter based on the FHM, which assures asymptotic stability and a prescribed H_∞ index for the filtering error system. A sufficient condition for the existence o such a filter is established through seeking the feasible solutions of a linear matrix inequality (LMI). Simulation example is provided to illustrate the design procedure of the proposed method.