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

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE