Abstract
This paper presents the application of a value-set-based graphical approach to robust stability analysis for the ellipsoidal families of fractional-order polynomials with a complex structure of parametric uncertainty. More specifically, the article focuses on the families of fractional-order linear time-invariant polynomials with affine linear, multilinear, polynomic, and general uncertainty structure, combined with the uncertainty bounding set in the shape of an ellipsoid. The robust stability of these families is investigated using the zero exclusion condition, supported by the numerical computation and visualization of the value sets. Four illustrative examples are elaborated, including the comparison with the families of fractional-order polynomials having the standard box-shaped uncertainty bounding set, in order to demonstrate the applicability of this method.
Highlights
Robustness plays a fundamental role in automatic control theory and practice [1,2,3,4]
To the best of the authors’ knowledge, it has been already published works dealing with robust stability of the spherical/ellipsoidal families of IO polynomials as well as works focused on the families of FO polynomials with box-shaped uncertainty bounding set, even with complicated uncertainty structure, but there are currently no works directly addressing the robust stability of spherical/ellipsoidal families of FO polynomials, except for potentially applicable techniques for more general infinite-dimensional systems
The spherical/ellipsoidal parametric uncertainty is always dependent by its definition, but it can still be combined with the independent uncertainty structure
Summary
Robustness plays a fundamental role in automatic control theory and practice [1,2,3,4]. To the best of the authors’ knowledge, it has been already published works dealing with robust stability of the spherical/ellipsoidal families of IO polynomials as well as works focused on the families of FO polynomials with box-shaped uncertainty bounding set, even with complicated uncertainty structure, but there are currently no works directly addressing the robust stability of spherical/ellipsoidal families of FO polynomials, except for potentially applicable techniques for more general infinite-dimensional systems. This paper is intended to deal with robust stability analysis of the ellipsoidal families of FO polynomials with complex parametric uncertainty structure, namely with affine linear, multilinear, polynomial, or general uncertainty structure. Science On-line Conference 2019 [10], 3rd Computational Methods in Systems and Software 2019 [11], and 30th International DAAAM Symposium [50]
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