  In this paper, some special Lorenz cones are constructed using Dikin
ellipsoid and some hyperplane. We also study the structure of the constructed
cones, especially the eigenvalues structure of the related matrix in the
formula of elliposid. These novel Lorenz cones which locate in positive orthant
by its construction are potential candidates to design invariant cone for a
given dynamical system. It provides more flexibility for practitioner to choose
more cones in the application for system stability analysis.

Dynamical Systems