On the stability of a class of polytopes of third order square matrices and stability radius (Q2771370)

The paper focuses on the computation of the robust stability radius of a matrix, a problem which has applications in control theory and stability analysis of linear dynamical systems affected by parametric uncertainty. The paper is very narrow in scope since it focuses on the specific case of a real 4 by 4 matrix whose entries dependent on 3 interval coefficients. By a straightforward application of the Routh-Hurwitz criterion, the author shows that the robust stability radius, i.e., the greatest level of uncertainty preserving stability of the uncertain matrix, can be computed with the help of linear programming. It must be emphasized that indeed, the general problem of checking stability of a matrix affected by interval uncertainty is a difficult problem in the sense that the available robust stability analysis algorithms have computational time which is an exponential function of the matrix dimension and the number of uncertain parameters. However, these algorithms are certainly applicable and efficient in the very specific low-dimensional case studied in this paper.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00044].