# Accession Number:

## AD0614483

# Title:

## SUPERPOSITION IN A CLASS OF NONLINEAR SYSTEMS

# Descriptive Note:

## Doctoral thesis

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS

# Personal Author(s):

# Report Date:

## 1965-03-01

# Pagination or Media Count:

## 66.0

# Abstract:

Many nonlinear systems can be interpreted as linear transformations between vector spaces under appropriate definitions for the vector operations on the inputs and outputs. The class of systems which can be represented in this way, is discussed here. This class, referred to as the class of homomorphic systems, is shown to include all invertible systems. Necessary and sufficient conditions on a noninvertible system such that it is a homomorphic system, are derived. A canonic representation of homomorphic systems is presented. This representation consists of a cascade of three systems, the first and last of which are determined only by the vector space of inputs and the vector space of outputs, respectively. The second system in the canonic representation is a linear system. Necessary and sufficient conditions are presented under which all of the memory in the system can be concentrated in the linear portion of the canonic representation. A means for classifying homomorphic systems, suggested by the canonic representation, is discussed. This means of classification offers the advantage that systems within a class differ only in the linear portion of the canonic representation. Applications of the theory are considered for a class of nonlinear feedback systems.

# Descriptors:

# Subject Categories:

- Numerical Mathematics