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# Accession Number:

## AD0647846

# Title:

## AN EQUIVALENT GAIN AND STOCHASTIC ANALYSIS FOR NONLINEAR SAMPLED-DATA CONTROL SYSTEMS.

# Descriptive Note:

## Doctoral thesis,

# Corporate Author:

## ILLINOIS UNIV URBANA DEPT OF ELECTRICAL ENGINEERING

# Report Date:

## 1956-01-01

# Pagination or Media Count:

##
147.0

# Abstract:

## In this thesis, a generalized equivalent gain function for nonlinear sampled-data control systems is defined and is specified to be the ratio of the z-transform of the crosscorrelation function of the system input and output signals to the z-transform of the autocorrelation function of the system input signal. Although this definition can be used to derive the usual describing function when the input is sinusoidal, it is not restricted to the sinusoidal case. Consequently, it is fundamentally an equivalent gain function in the sense originally proposed by R. C. Booton, and it is a nonlinear element representation more general than the usual describing function. In the past, the techniques of describing function analysis have been helpful in nonlinear analysis and have furnished valid results. The applications of these techniques can be extended with the generalized equivalent gain function. The sinusoidal describing function and the discrete describing function become special cases of the equivalent gain function when the input is restricted to sinusoidal variations and a sampled-data system is studied. The equivalent gain function can be used for general deterministic input systems and can also be used for systems with stochastic input signals.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#