Recursive Filtering for a Class of Discrete-Time Stochastic Nonlinear Systems Subject to State Delays and Packet Drops

Abstract

This paper investigates the recursive filter problem for a type of discrete-time stochastic nonlinear systems subject to both determinate state delays and packet loss. Takagi-Sugeno fuzzy model is introduced to deal with the nonlinearities in the system and random Bernoulli variables are utilized to depict the probability of packet loss. In the simultaneous consideration of system nonlinearities, state delays as well as missing measurements, the aim for the discussed filtering problem is to obtain a set of filter parameters over a finite-time horizon to minimize the upper bound of filtering error covariance. Via elaborate mathematical analysis, these desired filter parameters are derived by virtue of solving two Riccati-type difference equations, which are dependent on the latest estimation states and are with the online recursive form. Finally, the effectiveness of proposed design scheme is vividly inspected by an inverted pendulum system.