Functional interval observers for nonlinear fractional-order systems with time-varying delays and disturbances

Abstract

This article considers the estimation problem for a class of uncertain fractional-order systems with time-varying delays and disturbances, in which the time-varying delays are present in the state, while the disturbances are present in the output. A new design method of functional interval observers is proposed. In contrast to interval observers currently available in the literature, which dealt with integer-order systems or fractional-order systems without time delays, the functional interval observers with fractional-order [Formula: see text] in this article can deal with fractional-order time-delay systems and integer-order time-delay systems (when [Formula: see text]). Existence conditions of functional interval observers for non-linear fractional-order systems with time-varying delays are established and they are formulated in terms of linear programmings. Two algorithms are provided for determining the functional interval observers. Illustrative examples of the functional interval observer application are presented.