Diagonal stability of interval matrices and applications

Abstract: Let be an interval matrix and . We introduce the concept of Schur and Hurwitz diagonal stability, relative to the Hölder p-norm, of , abbreviated as and , respectively. This concept is formulated in terms of a matrix inequality using the p-norm, which must be satisfied by the same positive definite diagonal matrix for all . The inequality form is different for and . The particular case of is equivalent to the condition of quadratic stability of . The inequality is equivalent to the Stein inequality , and the inequality is equivalent to the Lyapunov inequality ; in both cases P is a positive definite diagonal matrix and the notation “” means negative definite. The first part of the paper provides and criteria, presents methods for finding the positive definite diagonal matrix requested by the definition of and , analyzes the robustness of and and explores the connection with the Schur and Hurwitz stability of . The second part shows that the or of is equivalent to the following properties of a discrete- or continuous-time dynamical interval system whose motion is described by : the existence of a strong Lyapunov function defined by the p-norm and the existence of exponentially decreasing sets defined by the p-norm that are invariant with respect to system’s trajectories. [Copyright &y& Elsevier]