Representations of jointly stationary stochastic feedback processes

Stable constant linear closed loop systems relating un input vector u to an output vector y and vice versa produce a. jointly stationary(y, u)process. On. The other hand it is often natural to split up a stationary vector random process z into component vectora y and z , and to examine the closed loop relations between y and u. This paper presents a number of now results on tho spectral factorization and tho closed loop representation of a jointly stationary vector (Y, u) process. Conditions am derived on the closed-loop models for thc joint process model to be of minimal degree, stable and minimum-phase. Relations between different joint process models producing the same spectrum Φ yu(z) arc established.