Interval observers for linear functions of states and unknown inputs of nonlinear fractional-order systems with time delays

The main objective of this paper is to design interval observers using the output signals and the delayed output signals to estimate the state vector and unknown input vector of nonlinear fractional-order systems with time delay. We first propose and design two new functional observers, such that they bound the set of all admissible values of a linear function of the state vector and the unknown input vector at each instant of time. We then derive conditions for the existence of interval functional observers and provide an effective design algorithm for computing unknown observer matrices. Finally, an example is given to show the effectiveness of the proposed design approach.