Some recent results on the design and implementation of interval observers for uncertain systems

Abstract Based on the theory of positive systems, the goal of interval observers is to compute sets of admissible values of the state vector at each instant of time for systems subject to bounded uncertainties (noises, disturbances and parameters). The size of the estimated sets, which should be minimised, has to be proportional to the model uncertainties. An interval estimation can be seen as a conventional point estimation (the centre of the interval) with an estimation error given by the interval radius. The reliable uncertainties propagation performed in this context can be useful in several fields such as robust control, diagnosis and fault-tolerant control. This paper presents some recent results on interval observers for several dynamical systems classes such as continuous-time and switched systems.