Positively invariant set of RFDE with applications to linear systems with time-varying input delays

Positively invariant set of retarded functional differential equations (RFDEs) with perturbations is investigated. As the application of results obtained for RFDEs, the state positively asymmetrical invariant set for linear systems with nonlinear time-varying input delay is first introduced, and sufficient conditions of the state positively asymmetrical invariant set for such systems are presented.