A note on the existence of positive realizations Original Research Article

The problem of existence of positive realizations for a class of continuous and discrete time systems is addressed and solved. It is shown that the existence of a (minimal) positive realization can be decided on the basis of two sub-matrices of the (infinite) Hankel matrix associated with the transfer function to be realized. Applications of this result to the problem of existence and construction of non-minimal realizations are also discussed.