Positive Interval System Dynamics Explored via Vertex Representatives vs. Vertex Majorizations

The paper explores the properties of positive interval dynamic systems in continuous-time, via two types of techniques, and develops a comparative study between the two approaches. The first type is based on the properties of the row and column representatives corresponding to the vertex set of the interval matrix A = [A^-, A⁺] ⊂ ℝ^n×n . The second type employs the properties of the dominant vertex A⁺ of the interval matrix. The results, separately derived for the two approaches, show the equivalence between the Hurwitz stability of matrix A⁺, the existence of several classes of Lyapunov functions, and the existence of several classes of exponentially decreasing sets that are positively invariant with respect to the interval system dynamics.