## 1 Introduction  
Robustness plays a fundamental role in automatic control theory and practice [1; 2; 3; 4]. Parametric uncertainty represents a natural, effective, but also a relatively simple tool for the mathematical description of real-life systems with potentially complex behavior (including nonlinearities, fast dynamics or changes in physical parameters) by means of linear time-invariant (LTI) models. The systems with parametric uncertainty are frequently given by so-called families of plants or families of polynomials, which have known structure but only imprecisely known parameters that are supposed to vary \"slowly\" within prescribed bounds. For example, the family of closed-loop characteristic polynomials is a typical object of interest. The crucial question is if a family of polynomials with parametric uncertainty remains stable for all possible variations of uncertain parameters. Thus, the methods for analyzing the robust stability of the systems with parametric uncertainty have been researched for several decades [5; 6]. The family of polynomials is determined by two main factors: its structure (especially the structure of uncertainty), and the uncertainty bounding set. There is a wide range of parametric uncertainty structures with various complexity, generality, and specific needs for their robust stability analysis. The uncertainty structures can be classified as independent, affine linear, multilinear, polynomic, and general [5; 7; 8; 9]. Moreover, the uncertainty needs to be quantified a priori in order to know its \"size\". For this purpose, three main types of the uncertainty bounding set can be utilized, namely,the vector of uncertain parameters can be bounded either by a box, or by an ellipsoid (a sphere as a specific case), or by a diamond [5]. Anyway, a box version is the most popular, but an ellipsoidal bound is also of great importance. The corresponding families of polynomials are called the ellipsoidal polynomial families [10; 11], or spherical polynomial families [5; 12; 13; 14; 15; 16; 17]. Strictly speaking, many works, e.g., [5; 12; 15], use the term \"spherical polynomial family\" solely for a family with the simplest independent uncertainty structure and uncertainty bounding set in the shape of an ellipsoid. In such a case, it can be considered as the analogy to the standard interval polynomial. However, the term \"spherical polynomial family\" or more frequently \"ellipsoidal polynomial family\" is used in more general meaning in this paper, i.e., for a family with any parametric uncertainty structure and uncertainty bounding set in the shape of a sphere or an ellipsoid, respectively. Thus, the term \"spherical/ellipsoidal polynomial family\" itself is considered not to give any information about the uncertainty structure, but only notifies that the family has a spherical/ellipsoidal uncertainty bounding set. The information about the uncertainty structure must be added. Note that the spherical/ellipsoidal parametric uncertainty itself is, by its definition, always dependent, but the (in)dependency of the uncertainty structure is discussed here. Despite the fact that the spherical/ellipsoidal parametric uncertainty has not been researched so often as the classical box-shaped parametric uncertainty, there is still a range of works dealing with the spherical/ellipsoidal parametric uncertainty and related problems, but, to the best of the authors' knowledge, only for integer-order (IO) systems and not for fractional-order (FO) systems yet, apart from the works addressing the more general infinite-dimensional systems, e.g., [18; 19]. Robust pole-placement technique for plants with ellipsoidally uncertain parameters, based on a convex minimax programming, was proposed in [20]. Connection of the identification (performed in the bounded-error context) and controller design (using \(H_{\infty}\) optimization) through ellipsoidal descriptions of parameter uncertainty was discussed in [21].