  Recently, barrier certificates have been introduced to prove the safety of
continuous or hybrid dynamical systems. A barrier certificate needs to exhibit
some barrier function, which partitions the state space in two subsets: the
safe subset in which the state can be proved to remain and the complementary
subset containing some unsafe region. This approach does not require any
reachability analysis, but needs the computation of a valid barrier function,
which is difficult when considering general nonlinear systems and barriers.
This paper presents a new approach for the construction of barrier functions
for nonlinear dynamical systems. The proposed technique searches for the
parameters of a parametric barrier function using interval analysis. Complex
dynamics can be considered without needing any relaxation of the constraints to
be satisfied by the barrier function.
