A New Observer Design for Fuzzy Bilinear Systems with Unknown Inputs

Abstract

An observer design for a class of nonlinear 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. A parallel distributed observer (PDO), which is constructed with local linear observers and the appropriate grade of the membership functions, is a conventional observer for Takagi-Sugeno fuzzy bilinear systems. However, it is known that its design conditions have conservativeness. In this paper, to reduce the conservatism in the design conditions, non-PDO with new design conditions is proposed. Our design conditions are derived from a multiple Lyapunov function, which depends on the membership function with time-delay in the premise variables. This method eventually reduces the conservatism and enables us to construct an observer for a wide class of nonlinear systems. When the premise variables are the state variables that are not measurable, Takagi-Sugeno fuzzy bilinear systems can represent a wider class of nonlinear systems. Hence, an observer design for fuzzy bilinear systems with unmeasurable premise variables is also proposed. Finally, numerical examples are given to illustrate our design methods.