Robust and simultaneous reconstruction of actuator and sensor faults for time delay system

Abstract

This paper considers the problems of robust and simultaneous actuator and sensor faults reconstruction for uncertain time-delay system based on sliding mode observer (SMO). The time-delay is bounded and affects the state of the system. In fact, taking into account the time-delay, obtaining a simultaneous actuator and sensor fault reconstruction is a difficult task. Therefore, to overcome this difficulty, a virtual augmented system is established in which the sensor fault in the real system is treated as pseudo-actuator fault. For this virtual augmented system, a new SMO design method is proposed. To obtain this observer, the SMO concept, a Lyapunov-Krasovskii approach and the Linear Matrix Inequality (LMI) optimization are derived to guarantee the stability of the estimation error dynamics and compute the SMO gains. A numerical example is given to illustrate the validity and the applicability of the proposed approaches.