Unknown Input Observer for Discrete-Time Fuzzy Bilinear Systems

An observer design for a class of discrete-time Takagi-Sugeno fuzzy bilinear systems with unknown inputs is considered. 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. For such systems, a design method for obtaining an observer that estimates the state of the system is proposed. Different from a design of a parallel distributed observer (PDO) which is constructed with local linear observers and the appropriate grade of the membership functions, non-PDO design is considered. A PDO is a conventional observer for Takagi-Sugeno fuzzy bilinear systems, and its design conditions have conservativeness. In this paper, in order to reduce the conservatism in the observer design conditions, non-PDO with novel design conditions is proposed. Our design conditions are based on a multiple Lyapunov matrix approach. This method eventually reduces the conservatism and enables us to construct an observer for a wide class of nonlinear systems. Finally, a numerical example is shown to illustrate our design methods.