Sliding mode observer for robust estimation of state and fault for linear uncertain systems

This paper describes a method for designing sliding mode observer for robust estimation of state and fault in a class of linear systems with uncertainty. A constrained Lyapunov equation must be met guaranteeing a stable sliding motion on the switching manifold that is insensitive to matched uncertainties and faults. This equation is solved by using Linear Matrix Inequalities (LMIs) techniques. A fault estimation approach is presented using output error injection where the estimation error is dependent on the bounds on the uncertainty and state observation error. This approach is able to estimate the shape and amplitude of fault, which is useful for fault accommodation purposes. Simulation results demonstrate the effectiveness of the design framework proposed in this paper.