# Accession Number:

## AD0730504

# Title:

## Identification and Modelling of Discrete, Stochastic Linear Systems.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CALIF STANFORD ELECTRONICS LABS

# Personal Author(s):

# Report Date:

## 1971-08-01

# Pagination or Media Count:

## 122.0

# Abstract:

The basic problem dealt with in the paper is the identification of stochastic, discrete, multivariable linear systems from input-output data. The problem definition includes the possibility of both deterministic and stochastic inputs, although all the noise sources are restricted to be gaussian and white. Using an innovations formulation of the maximum likelihood criterion, the author is able to obtain probability one convergence of the impulse response matrices to their true values. From these matrices one develops a canonical form for multivariable linear systems which requires no structural information or other prior knowledge of the system although the results are derived in such a way that such knowledge can certainly be used if it is available. This canonical form is also useful in the least squares identification of multivariable systems. One presents two very satisfactory methods of identifying the dimension of a system, one based on the whiteness of the resulting error process and the other based on the relative decrease of the cost function as input must satisfy to guarantee the probability one convergence of the impulse response matrices, and one points out easy methods of constructing input sequences which satisfy these conditions. Finally, one presents both a working program to perform the identification and suggestions, based on computational experience, for possible improvements. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability