## 1 Introduction
The similar problem of connecting the prediction error identification methods, which leads to ellipsoidal parametric uncertainty regions, and robust state feedback control was also presented in [22], but via linear matrix inequalities (LMIs). Before that, the paper [23] showed that robust stabilization of a scalar plant affected by ellipsoidal parametric uncertainty could be treated as a convex LMI problem. Furthermore, various identification and robust control methods for systems with ellipsoidal parametric uncertainty are addressed in [24; 25; 26; 27]. Looking more deeply to robust stability analysis of systems with parametric uncertainty and uncertainty bounding set in the shape of a sphere/ellipsoid, there are several techniques available in the literature. The Soh-Barger-Dabke theorem [5; 28] represents the method for spherical polynomial families with independent uncertainty structure, i.e., it is the spherical analogy to the classical Kharitonov theorem. Moreover, extensions that are applicable for solving the robust stability for closed-loop systems with affine linear structure of uncertainty are provided by the theorem of [PERSON] [5; 29] and by the theorem of [PERSON] [5; 30], which is based on the idea of the spectral set. Furthermore, well-known Tsypkin-Polyak criterion [31] can be utilized for testing the robust stability or rather for computing the robustness margin under spherical uncertainty. It should be noted that the spherical version of Tsypkin-Polyak criterion is directly connected with the results given by Soh-Berger-Dabke theorem [5]. There is a relative lack of robust stability analysis methods for systems with complicated structures of parametric uncertainty. Fortunately, the combination of the value set concept and the zero exclusion condition [5] is applicable for a wide range of uncertainty structures, including the most complex ones [7; 8; 32]. Its IO version [8] was extended to the FO cases in, e.g., [33; 34; 35; 36], and subsequently applied to the FO polynomials with complicated uncertainty structure (and standard box-shaped uncertainty bounding set) in [9]. The FO calculus [37; 38; 39] and its applications in many fields [40] have been intensively researched lately. Obviously, the area of control engineering has been deeply influenced by the FO calculus as well--remind just a few works among many others [41; 42; 43; 44; 45]. It is understandable that a combination of robust and FO control represents very attractive research direction nowadays--see the detailed literature review of robust stability analysis for FO LTI systems with parametric uncertainty in the introduction of the paper [9]. Besides the classical control systems, there is an interesting class of problems related to control of quantum systems that model the evolution characterizing physical phenomena at atomic scales [46; 47]. Naturally, the robustness of quantum control systems belongs among the studied topics as well [48; 49]. To sum up, 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. Therefore, 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. The investigation of the robust stability is performed by means of the graphical approach using the value set concept and the zero exclusion condition, which is exceptionally universal and which is applicable to the spherical/ellipsoidal families of IO or FO (as shown here) polynomials as well.