This paper considers the non-convex problem of finding the nearest Metzler
matrix to a given possibly unstable matrix. Linear systems whose state vector
evolves according to a Metzler matrix have many desirable properties in
analysis and control with regard to scalability. This motivates the question,
how close (in the Frobenius norm of coefficients) to the nearest Metzler matrix
are we? Dropping the Metzler constraint, this problem has recently been studied
using the theory of dissipative Hamiltonian (DH) systems, which provide a
helpful characterization of the feasible set of stable matrices. This work uses
the DH theory to provide a block coordinate descent algorithm consisting of a
quadratic program with favourable structural properties and a semidefinite
program for which recent diagonal dominance results can be used to improve
tractability.Comment: To Appear in Proc. of 56th IEEE CD
