This paper exploits the decentralized integral controllability (DIC) of stable negative-imaginary (NI) systems with non-singular DC-gain matrix to develop a constant input tracking framework with failure tolerance property in the event of sensor and/or actuator faults. By virtue of the DIC property of NI systems, it is shown that a positive feedback interconnection of two NI systems, of which one is a decentralized integrator system with non-negative gains and the other one is a stable NI system having negative definite DC-gain matrix, is internally stable. This is in contrast to the existing results where, for internal stability, at least one of the systems needs to be strictly negative-imaginary (SNI). Further it is shown that, in a positive feedback interconnection, stable NI systems with negative definite DC-gain matrix exhibit integral controllability (IC) property for any positive value of the integral gain k, which is a distinct property of stable NI systems having negative definite DC-gain matrix since the existing notion of IC for LTI systems offers only a finite range of k. Using the DIC property and the eigenvalue loci technique, some new results and research directions for the NI systems have also been presented in this paper. (C) 2018 Published by Elsevier Ltd.