Abstract : A dynamic system can often be described by a state equation ˙x = h(x, u, t)
where x ∈ Rn is the state vector, u ∈ Rm is the control vector and h :
Rn × Rp × R → Rn is the evolution function. Assume that the control low
u = g (x, t) is known (this can be obtained using control theory), the system
becomes autonomous. If we define f (x, t) = h(x, g (x, t) , t), we get the following
˙x = f (x, t) .
The validation of some stability properties of this system is an important and
difficult problem  which can be transformed into proving the inconsistency of a
constraint satisfaction problem. For some particular properties and for invariant
system (i.e., f does not depend on t), it has been shown  that the V-stability
approach combined interval analysis  can solve the problem efficiently. Here,
we extend this work to systems where f depends on time.