## 3 Parametric Uncertainty Structure  
The parametric uncertainty structure is given by the form of coefficient functions \(\rho_{i}(q)\) in (5). Generally, the more complicated coefficient functions and the more complicated interconnections among them mean the more complex task of the robust stability analysis. In other words, the level of complexity of \(\rho_{i}(q)\) is the deciding factor of the convenient robust stability analysis technique. The parametric uncertainty structures for IO systems can be classified as follows [5; 7; 8; 9]:  
* Independent uncertainty structure
* Affine linear uncertainty structure
* Multilinear uncertainty structure
* Polynomic uncertainty structure
* General uncertainty structure  
Moreover, there are some special cases, such as:  
* Single parameter uncertainty
* Retarded quasi-polynomials  
A relatively detailed description of these uncertainty structures (with emphasis on the uncertainty bounding set in the shape of a box) can be found in [9]. To summarize it:For the independent uncertainty structure, each uncertain parameter may enter into the one and only coefficient function. Nevertheless, the FO case of this \"independent\" uncertainty structure is more complex as the real and imaginary parts can be mutually dependent in fact, and consequently, the classical IO version of the Kharitonov theorem is not applicable for FO families [33].  
The affine linear uncertainty structure represents the scenario in which more parameters may enter into the same coefficient function, but the structure of the functions has to be affine linear one. A possible method for robust stability of a class of FO systems with affine linear uncertainty structure has been presented in [51].  
For the multilinear uncertainty structure, if all but one uncertain parameter are fixed, then the coefficient function becomes affine linear in this non-fixed parameter. In short, the coefficient functions may include the products of parameters. The robust stability of FO systems with multilinear uncertainty structure is solved, e.g., in [36].  
The polynomic structure of uncertainty means that the coefficient functions are represented by the multivariable polynomials in uncertain parameters. Investigation of robust stability is a nontrivial task. Formally, the polynomic structure can be transformed into the multilinear structure with a new uncertainty bounding set, but it is not much helpful from the viewpoint of robust stability investigation. [9]  
And finally, the general uncertainty structures contain the coefficient functions in the form of arbitrary multivariable functions of uncertain parameters under the assumption that the functions are continuous on relevant intervals. Generally, there are no analytical robust stability analysis tools available. [9]  
The mentioned classification of parametric uncertainty structures is independent of the shape of the uncertainty bounding set (see below), so it is valid also for spherical/ellipsoidal families of polynomials. Strictly speaking, the spherical/ellipsoidal parametric uncertainty is always dependent by its definition, but it can still be combined with the independent uncertainty structure.