Accession Number : AD0424994

Title :   EXISTENCE OF QUADRATIC TYPE LIAPUNOV FUNCTIONS FOR A CLASS OF NONLINEAR SYSTEMS,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS CRUFT LAB

Personal Author(s) : Narendra,Kumpati S. ; Goldwyn,Roger M.

Report Date : 01 AUG 1963

Pagination or Media Count : 29

Abstract : The contruction of Liapunov functions is presented non-linear systems related to the Lur'e problem. The method presented consists in developing a quadratic type Liapunov functioncalled a spanning Liapunov function (SLF)-for an associated linear system, and modifying it suitably for the nonlinear case. Using this approach, a theorem of Popov, for the Lur'e problem is derived and is extended to the case with m nonlinearities. Condition for the existence of a Liapunov function of this form for the case of a gain in the Lur'e problem are derived. The results are used to construct Liapunov functions for certain specific systems. (Author)

Descriptors :   (*SPECIAL FUNCTIONS (MATHEMATICAL), NONLINEAR SYSTEMS), TRANSFORMATIONS (MATHEMATICS), DIFFERENTIAL EQUATIONS, STABILITY

Distribution Statement : APPROVED FOR PUBLIC RELEASE