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 $\mathbb {A}=[A^{-}, A^{+}]\subset \mathbb {R}^{n\times n}$ 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.

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