Integral characterizations of uniform asymptotic and exponential stability with applications (Q1865838)

Integral characterizations of uniform global asymptotic stability (UGAS) and uniform global exponential stability (UGES) for time-varying differential inclusions are proved. These integral characterizations are used to conclude UGAS from uniform global stability (UGS) and suitable properties of the derivatives of a family of functions. As a corollary, a generalization of a theorem of Matrosov (on the use of a differentiable auxiliary function to conclude UGAS) is obtained. Moreover, it is shown how one can conclude UGAS from UGS for the system and UGAS for a system related to the original system through injection of an weakly uniformly integrable output function.