An Improved Unknown Input Observer Design for Fuzzy Bilinear Systems

An observer design for a class of nonlinear systems with unknown inputs is considered. Since Takagi-Sugeno fuzzy bilinear systems represent a wide class of nonlinear systems and these systems with unknown inputs are an ideal model for many physical systems, a design method to obtain an unknown input observer that estimates the state of the system with unknown input is proposed based on Takagi-Sugeno fuzzy systems. A parallel distributed observer(PDO), which consists of local linear observers with the appropriate grade of the membership functions, is a conventional observer for Takagi-Sugeno fuzzy bilinear systems, but its design conditions are known to be conservative. In this paper, to reduce the conservatism in the observer design conditions, non-PDO with new design conditions is proposed. Our design conditions are obtained from a multiple Lyapunov function, which depends on the integral of the membership function. This method drastically reduces the conservatism. Finally, a numerical example is given to illustrate our design methods.