Fault detection observer design for periodic piecewise linear systems

This article deals with the problem of fault detection observer design for continuous-time periodic piecewise linear systems. Mixed (Formula presented.) performance index is introduced, which results in a trade-off between robustness to unknown input and sensitivity to a fault. Based on a class of Lyapunov functions with time-varying Lyapunov matrices, sufficient conditions are developed to investigate the existence of periodic piecewise fault detection observer with weighted (Formula presented.) performance. A tractable iterative algorithm is proposed to establish the desired periodic piecewise fault detection observer. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.