
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 nonlineargain element is investigated. Sufficient conditions for secondorder and thirdorder systems of this type to be asymptotically stable inthelarge are determined through the use of the Lur'e Lyapunov function and the Aizerman linearization. For the secondorder case, the restriction on the nonlinear gain is that it be a singlevalued function bounded by the linear gains of zero and infinity. For the thirdorder case, the restriction on the nonlinear gain is that it be a singlevalued function bounded by the linear gains of zero and 8 alpha beta gamma where alpha, beta, and gamma are the real openloop 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