Investigation of robust stability for fractional-order LTI systems with multilinear structure of ellipsoidal parametric uncertainty

Abstract

The contribution focuses on the investigation of robust stability for fractional-order linear time-invariant (LTI) systems with the multilinear structure of ellipsoidal parametric uncertainty, i.e., the analyzed family of fractional-order polynomials has the multilinear uncertainty structure and an ellipsoid-shaped uncertainty bounding set. The robust stability test is based on the numerical calculation and subsequent plot of the value sets, and the application of the zero exclusion condition. Unlike the previously published works, this contribution shows that, contrary to the case of a two-dimensional ellipse of parameters, the internal points of a three-dimensional ellipsoid of parameters cannot create the boundary of the value set in the complex plane even under more complicated uncertainty structures, such as the multilinear one. © 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.