Hybrid filter design of fault detection for networked linear systems with variable packet dropout rate

The study focuses on the fault detection filter design problem for a class of networked systems with intermittent measurements. The fault detection filter, which is used as residual generator, is formulated as an ℋ_∞ filtering form. The random packet dropouts are governed by a Bernoulli distributed sequence, and the packet dropout rate is uncertain and variable, which is described by a semi-Markov stochastic process. A more general class of Lyapunov functions that not only depend on the system modes, but also on the staying time during the current system mode is utilised. Afterwards, numerically testable sufficient conditions on the existence of a desired fault detection filter are established such that the filtering error system is σ-error mean square stable with a prescribed ℋ_∞ disturbance attenuation level. Finally, an illustrative example is provided not only to demonstrate the effectiveness of the designed filter and the superiority of the utilisation of semi-Markov chain, but also the necessity of considering the variation of packet dropout rate in the design phase.