Interval functional observers for time-delay systems with additive disturbances

This article considers the design of interval functional observers to estimate a linear function of the state vector of time-delay systems subject to both input and output additive disturbances. Two novel functional observers are proposed and designed such that they bound the set of all admissible values of a linear function of the state vector at each instant of time. By contrast to interval observers currently available in the literature, both observers proposed in this article utilize multiple delayed output measurement and have a more general structure. This trade-off feature overcomes some drawbacks in previous work and enables interval functional observers to be designed for a wider class of time-delay systems. Conditions for the existence of interval functional observers are derived and an effective design algorithm for computing unknown observer matrices is provided. Two illustrative examples are given to show the advantages and effectiveness of our design method.