Reduced-Order Filter Design for a Class of Discrete-Time Nonlinear Systems with Multiple Sensor Faults

The reduced-order filtering problem for a class of discrete-time smooth nonlinear systems subject to multiple sensor faults is studied. It is well known that a smooth complex nonlinear system can be approximated by a Takagi-Sugeno fuzzy linear system with finite number of subsystems. In this work, firstly, the discrete-time smooth nonlinear system is transferred into a Takagi-Sugeno fuzzy linear system with finite number of subsystems. Secondly, a filter with the reduced order of the original system is proposed to be designed. Different from the traditional assumption in which the measurement of the output is ideal, the measurement of the output is subject to sensor faults which are described via Bernoulli processes. By using the augmentation technique, a stochastic Takagi-Sugeno filtering error system is obtained. For the stochastic filtering error system, the exponential stability and the energy-to-peak performance are investigated. Sufficient conditions which can guarantee the exponential stability and the performance are obtained. Then, with the proposed conditions, the design procedure of the filter for the nonlinear system is proposed. Finally, a numerical example is used to show the effectiveness of the proposed design methodology.