Distributed Recursive Filtering for a class of Discrete-time Stochastic Nonlinear Systems Subject to State Delays

This paper investigates the distributed recursive filtering problem for a type of discrete-time stochastic nonlinear systems subject to state delays as well as the communication topology of geographically distributed wireless sensors. The Takagi-Sugeno fuzzy model is introduced to deal with nonlinearities in system states and measurements. In the simultaneous consideration of system nonlinearities, state delays as well as topology, we aim to obtain a set of filter parameters over a finite-time horizon, minimizing the traces of permitted upper bounds for the filtering error covariance matrices. Via elaborate mathematical analysis, two sets of filter gains are derived in virtue of solving two Riccati-type difference equations, which are dependent on the latest estimation states and are with the online recursive form. In the end, the validity of the designed scheme is illustrated by an inverted pendulum system.