Faults reconstruction of delayed out put system using Sliding Mode Observer

In this paper, we propose a Sliding Mode Observer (SMO) design method to solve the problem of fault reconstruction for a class of linear systems with output time-delay. A sufficient conditions using Linear Matrix inequality (LMI) optimization and Lyapunov functional are derived to compute the SMO gains and guarantee the stability of the estimation error dynamics. Applying the developed SMO and the equivalent output error injection, actuator and sensor faults reconstructions are obtained. Therefore, these two problems of SMO design and faults reconstruction are numerically tractable via LMI optimization. Numerical example is given to illustrate the validity and the applicability of the proposed approaches.