Functional interval observer for the linear systems with disturbances

A Luenberger-like functional interval observer for the linear systems with time-varying disturbances is developed in this study. First, as an extension of the definition of the general interval observer, a new definition of the functional interval observer is provided. Then the sufficient conditions for the existence of such an observer are introduced in terms of the properties of positive systems. Simultaneously, on the basis of the proposed existence conditions, the parametric design method of the interval observer for the linear functional of the states in the systems is presented by employing the solution of the Sylvester equations. Eventually, the correctness and efficiency of the obtained results are illustrated by a numerical example.