Existence of Metzler Matrices with Given Spectra of Positive Stable Linear Systems and Electrical Circuits

Abstract

The problem of existence of Metzler matrices with given spectra is addressed for positive stable continuous-time linear systems and electrical circuits. Necessary and sufficient conditions for the existence of the Metzler matrices are established. It is shown that positive and stable electrical circuits have real eigenvalues. An open problem for positive electrical circuits is formulated. The considerations are illustrated by numerical examples of linear systems and positive electrical circuits.