Finite-time fault detection filter design for complex systems with multiple stochastic communication and distributed delays

This paper is concerned with the dissipative-based finite-time non-fragile fault detection filtering problem for a class of discrete-time complex systems with infinite distributed delay, randomly occurring multiple delays and channel fadings. In particular, the fading channel phenomena is described by Rice fading models. Further, the occurrence of the delays and channel fading phenomena are all assumed to be stochastic variables. To characterize and govern the random nature, few uncorrelated stochastic variables following the Bernoulli distribution are introduced. The implementation uncertainties are also considered in the design of the residual generator to alleviate the negative effects and to enhance the filter design. The stochastic analysis techniques together with Lyapunov stability theory are utilized to establish the sufficient conditions for the finite-time stochastic bounded of the augmented filtering error system. The desired filter gains are obtained by solving the linear matrix inequality based constraints. Finally, the numerical example demonstrates the applicability and efficacy of the fault detection filter design technique.