Robust Sliding mode observer for fault estimation of uncertain system Habib Ben Zina Research Unit on Control, Monitoring and Safety of Systems (C3S) High School of Sciences and Techniques of Tunis (ESSTT), 5, av. Taha Hussein, BP 56-1008 Tunis, Tunisia Email: habibbenzina@yahoo.fr Slim Dhahri Research Unit on Control, Monitoring and Safety of Systems (C3S) High School of Sciences and Techniques of Tunis (ESSTT), 5, av. Taha Hussein, BP 56-1008 Tunis, Tunisia Email: slim_dhahri@yahoo.fr Fayçal Ben Hmida Research Unit on Control, Monitoring and Safety of Systems (C3S) High School of Sciences and Techniques of Tunis (ESSTT), 5, av. Taha Hussein, BP 56-1008 Tunis, Tunisia Email: Fayçalbenhmida@esstt.rnu.tn Abstract—This paper describes a method of actuator fault estimation for linear uncertain systems. In this work, the upper bound of the unknown input is not required. To remove this requirement a modified sliding mode observer is presented. The novelty in this method lies in the structure of the mechanism introduced to calculate the sliding mode observer gain responsible to counteract uncertainty and actuator fault. In order to guaran- tee robustness to uncertainty, the developed observer use the  ∞ principle. Then, based on Lyapunov method, asymptotic stability conditions are given to design the observer parameters. Also, the equivalent output error injection signal is used to estimate the fault. Finally, the validity of this approach is illustrated by a VTOL aircraft model. Keywords: Sliding mode observer, LMI constraint, Robust fault estimation. I. I NTRODUCTION The basic idea of an FDI scheme is to generate an alarm when a fault occurs and also to identify the location of the fault.The fundamental purpose of an FDI is to reconstruct the output of reel systems and the estimation error is used as a residual. See [1], [2], [3], [4], [10]. One of source of error in state reconstruction is the deviation between the trajectory of real system and the predictions by its mathematical model. Moreover, disturbance signals exist in virtually all control applications and the effect of the problem generate the need to study observer design techniques that are robust to disturbances and model uncertainties despite the existence of perturbation. In recent years the sliding mode discontinuous approach to observer design has attracted significant attention [13], [15], [9]. The concept of the Sliding mode observer emerged from the Soviet Union in the late sixties. Using of a judicious control the system states could be forced to maintain a pre-defined surface in the state space that is insensitive to any disturbance or uncertainty which where implicit in the input channel. In[18], the authors introduced the use of the sliding mode approach in observer design and used lyapunov theory to prove stability. An alternative approach was proposed in [11] to the design of sliding mode observers using a discontinuous sliding term feedback through a suitable gain. [14] proposed a canonical sliding observer design using linear matrix inequalities (LMI). An SMO design method was proposed in [6]-[7] for a class of uncertain systems using some matching condition to decouple the effect of uncertainties from the fault signal system. In many cases the disturbances don’t verify any structural or geometric conditions and can corrupt the state estimation. To this end, in [9]-[19] the authors proposed a FDI scheme for a class of linear uncertain systems by minimizing the  2 gain from the uncertainties to the fault reconstruction. The aforementioned research has considered only the case where the bound of the unknown input is precisely known. However, there are many cases in which it is difficult to get information about the bound. This paper consider the design of SMO for robust state and fault estimation in linear uncertain systems that relax the requirement aforementioned. The robust observer design proposed in this paper use the  ∞ observer principle . We obtain an LMI condition using convex optimization to compute the observer gain. Also in the proposed SMO the structure of the variable structure gain is of reduced order when compared to the number of measurements. After solving the observer design problem we are interested in the problem of fault estimation by using the so called output error injection. The structure of this paper is arranged as follow:In section 1, we present the system and formulate the problem. In Section 2, we developed the design of the proposed SMO. A method for estimating the actuator fault is presented in section 3. In section 4, we show the effectiveness of modified SMO in actuator fault reconstruction by a numerical example. U.S. Government work not protected by U.S. copyright