Fault detection for 2-D hidden Markov jump systems: The Roesser model case

This work addresses the asynchronous fault detection issue for two-dimensional Markov jump systems. The state evolution of the concerned systems develops in two mutually perpendicular directions. And the asynchronicity between the system and the fault detection filter is accurately captured using a hidden Markov model. By the Lyapunov function approach, sufficient conditions are raised to allow the resultant 2-D Markov jump systems to be asymptotically mean-square stable and hold an H ∞ noise attenuation performance. At last, an example from the Darboux equation is furnished to reflect the correctness and effectiveness of the proposed scheme.