Asymptotic stability of time-varying switched systems under perturbations

In this paper, a new Liao-type of exponent is established to capture the long-term dynamics of nonlinear time-varying switched systems satisfying the linear growth condition. This new type of exponent is more general than current available result given in Dai et al. (2010) [5]. A sufficient condition for determining the asymptotic exponential stability of a class of quasi-linear switched systems is given, and the underlying switched systems may consist of infinitely many time-dependent subsystems.