Fault detection for a class of Markov jump systems with unknown disturbances

Abstract

An optimized fault detection observer is designed for a class of Markov jump systems with unknown disturbances. By reconstructing the system, the residual error dynamic characteristics of unknown input and fault signals, including unknown disturbances and modeling error are obtained. The energy norm indexes of disturbance and fault signals of the residual error are selected separately to reflect the restraint of disturbance and the sensitivity of faults, and the design of the fault detection observer is described as an optimization problem. By using the constructed Lyapunov function and linear matrix inequalities, a sufficient condition that the solution to the fault detection observer exists is given and proved, and an optimized design approach is presented. The designed observer makes the systems have stochastic stability and better capability of restraining disturbances, and the given norm index is satisfied. Simulation results demonstrate that the proposed observer can detect the faults sensitively, and the influence of unknown disturbance on residual error can be restrained to a given range.