Generalized diagonal stability of complex interval matrices relative to Hölder norms

The Schur, respectively Hurwitz, diagonal stability of a complex interval matrix C relative to a Hölder p-norm, 1 ≤ p ≤ ∞, abbreviated as SDSp, respectively HDSp, is defined in terms of a matrix inequality using the respective norm. This approach generalizes the SDSp, respectively HDSp, of real interval matrices previously studied by the same authors; it also incorporates, for p = 2, the standard concept of quadratic stability of complex interval matrices. The first part of the paper founds a qualitative-analysis framework that offers three SDSp, respectively HDSp, criteria for 1 ≤ p ≤ ∞, and investigates the existence of positive definite diagonal matrices required by the definition. The second part develops computational methods that test SDSp, respectively HDSp, for p ϵ {1,2, ∞} and provide concrete matrices satisfying the diagonal stability definition. All through the paper, the Schur and Hurwitz cases are addressed in parallel, both for concision reasons and for outlining the similarities. A relevant example illustrates the key elements of our results.