Interval observers for linear functions of state vectors of linear fractional‐order systems with delayed input and delayed output

Abstract

SummaryThis paper addresses the problem of interval observer design for linear functions of state vectors of linear fractional‐order systems, which are subjected to time delays in the measured output as well as the control input. By using the information of both the delayed output and input, we design two linear functional state observers to compute two estimates, an upper one and a lower one, which bound the unmeasured linear functions of state vectors. As a particular case with output delay only, we design a linear functional state observer to estimate (asymptotically) the unmeasured linear functions of state vectors. Existence conditions of such observers are provided, and some of them are translated into a linear programming problem, in which the observers' matrices can be effectively computed. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality, and effectiveness of the proposed design method.