
Accession Number : AD0433982
Title : GENERATION OF QUADRATICTYPE LIAPUNOV FUNCTIONS FOR LINEAR TIMEVARYING 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 timevarying 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 timevarying 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 VV phase plane yields further insight into the problem of stability and leads to the generation of Liapunov functions for an additional class of timevarying systems. In the final section this approach is compared with the wellknown 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