A survey of interval observers design methods and implementation for uncertain systems

The goal of the interval observers is to deal with the large but bounded uncertainties and disturbances by determining certain interval (upper and lower estimates) for the system states at each time instant. The mean of the interval that should be minimized can be considered as the point-wise estimate whereas the interval width provides the admissible deviation from that value. Thus, an interval estimation error bound is provided at any time instant that converges to zero in the absence of exogenous signals. Interval observers can be used in a wide range of applications because of its reliable uncertainties propagation such as robust control of linear and non-linear systems, fault detection and isolation, anti-disturbance controller design and so on. This paper presents some of the basic concepts and recent results obtained to design interval observers for uncertain systems like discrete-time, continuous-time, Linear Parameter Varying (LPV) systems and multiagent/interconnected systems. In addition, it also presents a brief discussion of the main approaches with some future recommendations. ? 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.