Stability Analysis of Linear Interval Systems: Polynomial vs. Matrix Approach

This paper addresses the issue of stability robustness for linear dynamical systems described by interval matrices. We briefly review two different approaches available, namely polynomial approach and matrix approach. In the polynomial approach, the interval matrices are converted to interval polynomials and the stability tested by the available methods on the Burwitz invariance of a family of polynomials out of which the most noteworthy being the "Kharitonov" test. In the matrix approach, the analysis is done directly in the matrix domain using methods such as the Elemental Perturbation Bound Analysis presented by the author (which uses Lyapunov theory as a tool), Gershgorin\´s diagonal dominance approach as well as some indirect methods involving the testing of definiteness of a matrix function. It is shown with the help of an example that the "elemental" bound approach turns out to be successful in predicting the stability while the polynomial approach fails to do so.