  We consider a generalised non-commutative space-time in which
non-commutativity is extended to all phase space variables. If strong enough,
non-commutativity can affect stability of the system. We perform stability
analysis on a couple of simple examples and show that a system can be
stabilised by introducing quartic interactions provided they satisfy
phase-space copositivity. In order to conduct perturbative analysis of these
systems one can use either canonical methods or phase-space path integral
methods which we present in some detail.
