GENERAL LEMMAS FOR STABILITY ANALYSIS OF LINEAR CONTINUOUS-TIME SYSTEMS WITH SLOWLY TIME-VARYING PARAMETERS

This note investigates stability conditions for some dynamic systems w ith slowly time-varying parameters or with unknown internal or externa l disturbances. The models and conditions are motivated by adaptive co ntrol problems. The results presented here provide some sufficient con ditions for the exponential convergence of the state sequence of syste ms without system disturbance, and for the uniform boundedness of the state sequence of such systems when they are subject to uniformly boun ded system disturbances.