Design of unknown input integral sliding-mode discrete observer for linear systems

This paper considers the problem of the observer design to estimate the state and reconstruct the unknown inputs for linear discrete-time systems in the presence of uncertainties. By appropriate use of system transformation and the integral term in the sliding-surface design, we propose a novel output injection term in its structure to achieve convergence of the sliding-manifold. The dimension of the designed observer is independent of the number of additive uncertainties in the model of the plant. A numerical simulation demonstrates the design procedure and compares the proposed observer with the standard proportional integral observer (PIO) design.