Abstract
The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition.
Highlights
Fractional order control represents promising and attractive research topic, which has been widely studied recently
This article presents a graphical approach to the robust stability analysis of families of fractional order polynomials with a particular emphasis on families of polynomials with complicated uncertainty structure based on plotting the numerically obtained value sets and utilization of the zero exclusion condition
This article was focused on a graphical approach to robust stability investigation for families of fractional order polynomials or even quasi-polynomials with complicated uncertainty structure
Summary
Fractional order control represents promising and attractive research topic, which has been widely studied recently. The necessary and sufficient condition for the interval FO-LTI systems was derived e.g. in [43] by using a complex Lyapunov inequality or in [44] in terms of linear matrix inequalities Both these works considered only the case of fractional order α 2 [1, 2) and some further papers were focused on the α 2 (0, 1) case–see e.g. This article presents a graphical approach to the robust stability analysis of families of fractional order polynomials (which can be considered as characteristic polynomials of investigated fractional order systems) with a particular emphasis on families of polynomials with complicated uncertainty structure based on plotting the numerically obtained value sets and utilization of the zero exclusion condition.
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