# Accession Number:

## AD0773188

# Title:

## On the Analysis of Feedback Systems with a Multipower Open Loop Chain

# Descriptive Note:

## Interim rept.

# Corporate Author:

## MICHIGAN UNIV ANN ARBOR SYSTEMS ENGINEERING LAB

# Personal Author(s):

# Report Date:

## 1973-10-01

# Pagination or Media Count:

## 43.0

# Abstract:

The report analyses the input-output behavior of feedback systems whose open loop map can be modeled by an operator, K, defined on a Hilbert space. In particular, attention is focused on the case where K is multipower, bounded, and strictly causal. The analysis uses Hilbert resolution space, the causality structure of K and contraction mapping techniques. The main objective is to clarify questions of the following type 1 Given an input, y, is the output, x, well defined. Existence, Uniqueness 2 If x is well defined, what can be said about the mapping y to x. Causality, Continuity 3 Given y how can x be computed. Computational method. To illustrate the difficulty associated with questions of this type, it is shown that a system input with a finite energy may generate an infinite energy, possibly with a finite escape time, feedback system output. Modified author abstract

# Descriptors:

# Subject Categories:

- Theoretical Mathematics