GENERATION OF QUADRATIC-TYPE LIAPUNOV FUNCTIONS FOR LINEAR TIME-VARYING SYSTEMS,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 22, 1963
- Accession Number
- AD0433982
Entities
People
- K. S. Narendra
- R. M. Goldwyn
Organizations
- Harvard University