Structural decomposition of transfer matrix of positive normal hybrid systems

A new class of positive normal hybrid linear systems is introduced. It is shown that: 1) the inverse matrix of the characteristic system matrix is normal if and only if its greatest common divisor of (n - 1)-th order minors is equal to one, 2) the rational matrix is normal if and only if its McMillan polynomial is equal to the last common denominator, 3) the rational matrix has the structural decomposition of its transfer matrix if and only if the transfer matrix is normal. A procedure for computation of the structural decomposition of a normal transfer matrix is proposed. The considerations are illustrated by numerical examples.