Spectral factorization for distributed parameter systems

The spectral factorization problem plays a central role in feedback control system design for linear time invariant lumped and distributed parameter systems. In particular, it constitutes an essential step in the solution of the linear-quadratic optimal control problem for infinite-dimensional state-space systems with bounded or unbounded control and/or observation operators. This paper is devoted to the solution of the multivariable spectral factorization problem in the framework of the Callier-Desoer algebra of possibly unstable distributed parameter system transfer functions, i.e. for multivariable distributed parameter systems with an impulse response admitting possibly an infinite number of delayed impulses. Criteria for the existence of such spectral factors are reported