Accession Number : AD0254578

Title :   SUFFICIENT CONDITIONS FOR THE STABILITY OF CERTAIN NONLINEAR CONTROL SYSTEMS

Corporate Author : CALIFORNIA UNIV BERKELEY ELECTRONICS RESEARCH LAB

Personal Author(s) : WILLIAMS, I.J.

Report Date : 25 JAN 1961

Pagination or Media Count : 1

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 Lur'e 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)

Descriptors :   *SERVOMECHANISMS, CONTROL SYSTEMS, FUNCTIONS(MATHEMATICS), MATHEMATICAL ANALYSIS, NONLINEAR DIFFERENTIAL EQUATIONS, NONLINEAR SYSTEMS, STABILITY.

Distribution Statement : APPROVED FOR PUBLIC RELEASE