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

摘要

In this report the existence of "Common Liapunov Functions" (CLF'S) -for linear time-varying systems is discussed.nFor 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.