Stability Analysis of Linear Systems via Transforming the Characteristic Polynomial Model to the Eigenvalue Problem under Interval Uncertainties

The paper addresses the stability analysis of linear continuous systems under interval uncertainties. This problem initially described by the characteristic polynomial is transformed into a corresponding eigenvalue problem. The final analysis is equivalent to estimating the eigenvalues of matrices which elements are nonlinear functions of interval parameters. A method for obtaining the exact range of the eigenvalues is used. It can be applied if certain monotonicity conditions are fulfilled. The method appeals to computing tight outer bounds on the eigenvalues range. The outer bounds are obtained as a solution of an algebraic nonlinear system. A numerical example, illustrating the applicability of the methods presented, is solved in the end of the paper. It is a linear system for fine position of object with big weight and inertness.