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 equation. ˙x = f (x, t) . The validation of some stability properties of this system is an important and difficult problem [2] 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 [1] that the V-stability approach combined interval analysis [3] can solve the problem efficiently. Here, we extend this work to systems where f depends on time.