Fault tolerant control and detection of networked control systems with Markov packet dropouts

This paper presents the design method of fault tolerant controller and fault detection observer for Networked Control Systems (NCSs) with packet dropouts governed by a Markov chain. The packet dropouts are transformed into the networked induced time delays because of the consideration of some late arrival packets. The closed-loop NCSs with an observer-based feedback controller and time-delay outputs is transformed into a Markov system with stated delays. Two criteria are developed to evaluate the performance of detecting the faults. Sufficient conditions on the existence of controllers and observers for the mean square stability with an H_- fault sensitivity level and an H_∞ disturbance attenuation level are derived through a Lyapunov function dependent on the upper bound of the number of consecutive packet dropouts. Such conditions are straightforwardly solved to obtain the strict linear matrix inequalities.