Unknown Input Observer for Takagi-Sugeno Fuzzy Bilinear System with Input and Output Disturbances

An estimation of the state variables for systems with disturbances is an important problem. In a practical situa- tion, not all the state variables are measurable, and disturbance noises come into the system. Especially, it is difficult to estimate the state variables of complicated nonlinear systems with input and output disturbances. In this paper, observer design methods for a discrete-time Takagi-Sugeno fuzzy bilinear system with unknown inputs and input/output disturbances are proposed. Our observer filters out unknown input and estimates the state and input/output disturbances of the system. Since Takagi- Sugeno fuzzy bilinear system represents a quite large class of nonlinear systems, an unknown input observer that estimates the state and input/output disturbance of Takagi-Sugeno fuzzy bilinear system with unknown inputs and disturbances is essential in many engineering fields. Observer design has started with a parallel distributed observer(PDO), which is constructed with local linear observers and the appropriate grade of the membership functions. However, design conditions for PDO are very conservative. To overcome such disadvantage, non- PDO with multiple Lyapunov matrices technique is proposed to design our observer in this paper. Such a design method is based on a multiple Lyapunov function with a sum of the membership functions. This method drastically reduces the conservatism. To demonstrate the validity of our proposed observer design approach, an illustrative numerical example is provided. Lastly, we end with concluding remarks.