Showing papers by "Michel Gevers published in 1981"

Representations of jointly stationary stochastic feedback processes

Abstract: Stable constant linear closed-loop systems relating an input vector u to an output vector u and vice versa produce a jointly stationary (y, u)-procoss. On the other hand it is often natural to split up a stationary vector random process z into component vectors yand u, and to examine the closed-loop relations between y and u. This paper presents a number of new results on the spectral factorization and the closed-loop representation of a jointly stationary vector (y, u)-proccss. Conditions are derived on the closed-loop models for the joint process model to bo oE minimal degree, stable and minimum-phase. Relations between different joint process models producing the same spectrum φyu(z)are established.

On multivariable pole- zero cancellations and the stability of feedback systems

Abstract: We study conditions for pole-zero cancellation including unstable pole-zero cancellation in the product of two transfer function matrices G and H. Pole-zero cancellation is defined using McMillan degree ideas, and conditions for cancellation are phrased in terms of the coprimeness of matrices associated with matrix fraction descriptions of G and H. Using the condition for unstable pole-zero cancellation, we obtain a new set of conditions for the stability of linear MIMO feedback systems. We show that such a feedback system is stable if and only if there is no unstable pole-zero cancellation in GH and if (I+GH)^{-1} is stable. On the other hand, if there is no unstable pole-zero cancellation in GH and any or all of (I+ HG)^{-1}, G(I+ HG)^{-1} , and H(I+ GH)^{-1} are stable, the closed-loop may be unstable- but only if there is an unstable pole-zero cancellation in HG.