Growth rate conditions for uniform asymptotic stability of cascaded time-varying systems

In the last decade several results on cascaded autonomous systems have appe ared in the literature. The sufficient conditions for the stability and sta bilizability of these systems are often related to certain growth rate cond itions on the functions which define the dynamics of the system. In this pa per we analyze three complementary classes of nonlinear time-varying system s according to these growth rates. For each case. we give further results t o guarantee uniform global asymptotic stability of the cascade and relate o ur contributions to input-to-state stability and other growth rate conditio ns previously reported. The advantage of this type of analysis is that it i s often easier to verify such conditions than to find a Lyapunov function w ith a negative-definite derivative. (C) 2001 Published by Elsevier Science Ltd.