On a new class of realization formulas and their application Original Research Article

A new set of realization formulas is derived for a class of matrix-valued functions W(λ). These include the standard realization formulas for rational W(λ). Observability, controllability, and minimality are defined and characterized. Conditions for W(λ) to be (J1, J2) isometric and/or (J1, J2) coisometric with respect to a pair of signature matrices J1 and J2 are given in terms of the realizations. Minimal factorizations for square W(λ) are considered, and formulas for the factors are deduced. Associated reproducing kernel spaces (of pairs too) are discussed.