Construction of Lorenz Cone with Invariant Cone Using Dikin Ellipsoid for Dynamical Systems

TL;DR

This paper introduces a method to construct Lorenz cones using Dikin ellipsoids and hyperplanes, offering new tools for invariant cone design in dynamical system stability analysis.

Contribution

It presents a novel construction of Lorenz cones with potential applications in invariant cone design for dynamical systems.

Findings

Constructed Lorenz cones using Dikin ellipsoid and hyperplanes.

Analyzed the eigenvalue structure of related matrices.

Proposed cones are suitable for system stability analysis.

Abstract

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.