Stability of time-varying nonlinear switching systems under perturbations

Recently, switched systems have been found in many practical applications such as in communication network dynamics, robot manipulators, traffic management, etc. In this paper, we study the stability of time-varying linear switched systems under perturbations that satisfy linear growth condition, which is not available in current literature. By introducing a new Liao-type exponent for time-varying linear switched systems, we generalize our recent result given in [5], and provide a sufficient condition of exponential stability for quasi-linear switched systems. The criterion of asymptotic stability is computable and is applicable to switched systems that may consist of infinitely many timedependent subsystems.