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Abstract A well-known characterization by Kraaijevanger [14] for Lyapunov diagonal stability states that a real, square matrix A is Lyapunov diagonally stable if and only if A ∘ S is… Click to show full abstract
Abstract A well-known characterization by Kraaijevanger [14] for Lyapunov diagonal stability states that a real, square matrix A is Lyapunov diagonally stable if and only if A ∘ S is a P -matrix for any positive semidefinite S with nonzero diagonal entries. This result is extended here to a new characterization involving similar Hadamard multiplications for simultaneous Lyapunov diagonal stability on a set of matrices. Among the main ingredients for this extension are a new concept called P -sets and a recent result regarding simultaneous Lyapunov diagonal stability by Berman, Goldberg, and Shorten [2] .
Journal Title: Linear Algebra and its Applications
Year Published: 2017
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