Decomposition of the Controllability and Observability Matrices Into Symmetrical and Asymmetrical Parts in Linear Electrical Circuits

Decomposition of the controllability and observability matrices into symmetrical and asymmetrical parts of electrical circuits composed of resistors, coils, capacitors and voltage sources are addressed. It is shown that: 1) the Metzler matrix is Hurwitz if and only if its symmetrical part is Hurwitz; 2) if the linear electrical circuit is controllable (observable) then at least its symmetrical or asymmetrical part is controllable (observable).