H∞ Filter Design for Fuzzy Bilinear Systems with Unknown Inputs and Disturbances

The H-infinity filter design for a class of bilinear systems with unknown inputs and external disturbances is considered. Takagi-Sugeno fuzzy bilinear system represents a wide class of nonlinear systems, and the system with unknown inputs and external disturbances is a practical model for many physical systems. For such a system, a design method for obtaining a filter that estimates the state of the system and attenuates the disturbance is proposed. Although the parallel distributed filter (PDF) is frequently used, a new class of non-PDF filters is introduced for Takagi-Sugeno fuzzy bilinear systems. Our design conditions are derived from a multiple Lyapunov function, which depends on the integral of the membership function. This method eventually reduces the conservatism and enables us to construct a filter for a wide class of nonlinear systems. Finally, a numerical example is given to illustrate our design methods.