Design of high-gain observers based on sampled measurements via the interval arithmetic

The main objective of this paper is to implement a high-gain “practical” observer with the interval arithmetic in the case of sampled measurements. In order to pursue this objective, two closed-form expressions are proposed to compute certified bounds on the solution of a single-input linear system, with distinct, real, and negative eigenvalues, when both the initial condition and the control input lie in given intervals. Furthermore, it is shown how such formulas can be extended in the case of sampled input measurements. These results are used to design an interval high-gain observer for non-linear systems in observer normal form. In particular, it is shown how to implement a high-gain “practical” observer with the interval arithmetic, both in continuous-time and in discrete-time, so to compute guaranteed interval estimates of the state of the system.