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.

Keywords

• Takagi–Sugeno fuzzy model
• nonlinear system
• bilinear system
• observer design
• unmeasurable premise variable