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

This paper studies fuzzy hyperbolic H_∞ filter for signal estimation of nonlinear continuous-time systems with unknown bounded disturbances. The fuzzy hyperbolic model (FHM) is a universal approximator, and can be used to establish models for 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 continuous-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 of such a filter is established through seeking the feasible solutions of a linear matrix inequality (LMI). Under the position and the dimension criteria, a new LMI condition is obtained to reduce the conservativeness for the analysis and design of fuzzy H_∞ filler based on extended ε-block and λ-block and the corresponding equivalent forms. Simulation examples arc provided to illustrate the design procedure of the proposed method.