# Accession Number:

## AD0254578

# Title:

## SUFFICIENT CONDITIONS FOR THE STABILITY OF CERTAIN NONLINEAR CONTROL SYSTEMS

# Descriptive Note:

# Corporate Author:

## CALIFORNIA UNIV BERKELEY ELECTRONICS RESEARCH LAB

# Personal Author(s):

# Report Date:

## 1961-01-25

# Pagination or Media Count:

## 1.0

# Abstract:

The stability of control systems containing one nonlinear-gain element is investigated. Sufficient conditions for second-order and thirdorder systems of this type to be asymptotically stable in-the-large are determined through the use of the Lure Lyapunov function and the Aizerman linearization. For the second-order case, the restriction on the nonlinear gain is that it be a single-valued function bounded by the linear gains of zero and infinity. For the third-order case, the restriction on the nonlinear gain is that it be a single-valued function bounded by the linear gains of zero and 8 alpha beta gamma where -alpha, -beta, and -gamma are the real open-loop pole locations of the system. If alpha, beta, and gamma are all equal, then the upper bound of 8 alpha beta gamma corresponds to the maximum linear gain for which the linearized system is stable. Author