Diagonal stability of interval matrices and applications (original) (raw)

P is a positive definite diagonal matrix and the notation "≺ 0" means negative definite. The first part of the paper • provides SDS p and HDS p criteria, • presents methods for finding the positive definite diagonal matrix requested by the definition of SDS p and HDS p , • analyzes the robustness of SDS p and HDS p and • explores the connection with the Schur and Hurwitz stability of A I . The second part shows that the SDS p or HDS p of A I is equivalent to the following properties of a discrete-or continuous-time dynamical interval system whose motion is described by A I : • 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.