Fault-Tolerant Reduced-Order Asynchronous Networked Filtering of 2-D Bernoulli Jump Systems

This article is devoted to asynchronous networked filtering against sensor failures for a class of two-dimensional (2-D) Bernoulli jump systems. The purpose is to design a fault-tolerant reduced-order asynchronous (FTROA) filter that ensures asymptotic mean-square stability and $\mathcal {H}_{2}$ disturbance-attenuation performance for the resulting filtering error system, characterized by a bi-mode-jumping property. A hidden Bernoulli model is adopted to characterize asynchronous mode switching between the original 2-D system and the designed filter. A sufficient condition on the stability and $\mathcal {H}_{2}$ performance is proposed. Based on the condition, a method of the needed FTROA filter is developed in terms of linear matrix inequalities by introducing an order-dependent slack matrix. Considering the calculation complexity, an alternative filter design is further presented by resorting to suitable matrix splittings and the projection theorem. Compared to the former, the latter is shown to be capable of significantly mitigating the computational burden while maintaining the desired performance. Finally, an actual example concerning the metal rolling process is provided to verify the effectiveness of the presented filter design methods.