INNER-OUTER FACTORIZATION FOR NONSQUARE PROPER FUNCTIONS WITH INFINITE AND FINITE J-OMEGA-AXIS ZEROS

The inner-outer factorization of a non-square proper function which ha s infinite and finite j omega-axis zeros and has no poles in the open right-half plane is studied in this paper via the concept of an infini te zero compensator. For a stabilizable and detectable realization of the above function with full normal column rank, the eigenstructures o f the system matrix pencils of the function and its spectral density m atrix are discussed based on Kronecker's theory, and a simple state-sp ace solution to the inner-outer factorization is given via the solutio ns of the generalized eigenvalue problems in terms of the original rea lization of the function.