Stability analysis of interacting dark energy models generally divides its parameters space into two regions : ( i ) w _ { x } \geq - 1 and \xi \geq 0 and ( ii ) w _ { x } \leq - 1 and \xi \leq 0 , where w _ { x } is the dark energy equation of state and \xi is the coupling strength of the interaction .
Due to this separation , crucial information about the cosmology and phenomenology of these models may be lost .
In a recent study it has been shown that one can unify the two regions with a coupling function which depends on the dark energy equation of state .
In this work we introduce a new coupling function which also unifies the two regions of the parameter space and generalises the previous proposal .
We analyse this scenario considering the equation of state of DE to be either constant or dynamical .
We study the cosmology of such models and constrain both scenarios with the use of latest astronomical data from both background evolution as well as large scale structures .
Our analysis shows that a non-zero value of the coupling parameter \xi as well as the dark energy equation of state other than ‘ -1 ’ are allowed .
However , within 1 \sigma confidence level , \xi = 0 , and the dark energy equation of state equal to ‘ -1 ’ are compatible with the current data .
In other words , the observational data allow a very small but nonzero deviation from the \Lambda -cosmology , however , within 1 \sigma confidence-region the interacting models can mimick the \Lambda -cosmology .
In fact we observe that the models both at background and perturbative levels are very hard to distinguish form each other and from \Lambda -cosmology as well .
Finally , we offer a rigorous analysis on the current tension on H _ { 0 } allowing different regions of the dark energy equation of state which shows that interacting dark energy models reasonably solve the current tension on H _ { 0 } .