Accession Number : AD0433982

Title :   GENERATION OF QUADRATIC-TYPE LIAPUNOV FUNCTIONS FOR LINEAR TIME-VARYING SYSTEMS,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS CRUFT LAB

Personal Author(s) : Narendra,K. S. ; Goldwyn,R. M.

Report Date : 22 NOV 1963

Pagination or Media Count : 25

Abstract : In this report the existence of Common Liapunov Functions (CLF'S) for linear time-varying systems is discussed. For a negative feedback system with G (s) in the forward path and a gain k (t) in the feedback path, it is shown that a sufficient condition to ensure the existence of CLF and hence stability is that 1/k + G(s) be a positive real function. For specific time-varying systems, Liapunov functions that are explicit functions of time are found to increase the stability range of a parameter over that given by the CLF. An analysis of the behavior of the Liapunov function V in the V-V phase plane yields further insight into the problem of stability and leads to the generation of Liapunov functions for an additional class of time-varying systems. In the final section this approach is compared with the well-known Floquet Theory for periodic systems. (Author)

Descriptors :   (*SPECIAL FUNCTIONS (MATHEMATICAL), LINEAR SYSTEMS), TIME, STABILITY, FEEDBACK, CONTROL SEQUENCES, ANALYTIC GEOMETRY, MOTION

Distribution Statement : APPROVED FOR PUBLIC RELEASE