An Improved Unknown Input Observer Design for Disrete-Time Fuzzy Bilinear Systems

Design methods of an observer for a discrete-time Takagi-Sugeno fuzzy bilinear system with unknown inputs is proposed. Takagi-Sugeno fuzzy bilinear system describes a large class of nonlinear systems and this system with unknown inputs even represents a realistic model for most practical systems. An unknown input observer that estimates the state of Takagi-Sugeno fuzzy bilinear system with unknown input is proposed based on multiple Lyapunov matrices. For fuzzy systems, a parallel distributed observer (PDO), which is constructed with of local linear observers and the appropriate grade of the membership functions, has been used, but its design conditions are eventually conservative. To reduce such conservativeness in observer design conditions, non-PDO with multiple Lyapunov matrices technique is proposed in this paper. Such a design method is based on a multiple Lyapunov function with double sum of the membership functions. In order to show the effectiveness of our proposed approach, a simple example is given. Finally, concluding remarks are given. Copyright (c) 2023 The Authors.