Reliable Filtering for Discrete-Time Nonlinear Systems via Innovation Constraints

This paper is concerned with the reliable filtering for discrete-time nonlinear systems with abnormal measurements and probabilistic distributed time-delays. Two binary stochastic sequences are employed to model stochastic occurring nonlinearities and probabilistic distributed time-delays, respectively. The considered abnormal measurements could be outliers or injected data resulting from cyber-attackers. A factitious saturation constraint on innovation is adopted to remove these abnormal measurements in the designed filter. By resorting to the stochastic analysis combined with Lyapunov stability theory, a sufficient condition is proposed to check whether or not the augmented system is bounded in mean square. Furthermore, the desired filter gain depends on the solution of a linear matrix inequality. Finally, an illustrative example is adopted to verify the effectiveness of the developed design scheme.