Power-Rate Global Stability of Dynamical Systems With Unbounded Time-Varying Delays

In this brief, dynamical systems with unbounded time-varying delays are investigated. Two approaches are developed to derive sufficient conditions ensuring the existence, uniqueness of the equilibrium and its global stability. Moreover, different from globally asymptotical stability and globally exponential stability, a new concept of stability, global power stability, is proposed. Under mild conditions, we prove that the dynamical systems with unbounded time-varying delays are globally power stable.