H_∞ fault detection for discrete-time hybrid systems via a descriptor system method

This paper solves the problem of fault detection for discrete-time hybrid systems via a descriptor system method. These systems include control inputs, unknown bounded disturbances, and sensor faults. Based on the descriptor system method, a fault detection observer is designed to obtain the estimation of the states, outputs and faults, simultaneously. By means of the observer gain, the state error system is stochastically stable, and the disturbances effect on the residuals meets the H_∞ performance index. The satisfactory sensitivity problem of the residuals to the faults is solved. A numerical example illustrates the effectiveness and applicability of the developed method.