  Computing the viability kernel is key in providing guarantees of safety and
proving existence of safety-preserving controllers for constrained dynamical
systems. Current numerical techniques that approximate this construct suffer
from a complexity that is exponential in the dimension of the state. We study
conditions under which a linear time-invariant (LTI) system can be suitably
decomposed into lower-dimensional subsystems so as to admit a conservative
computation of the viability kernel in a decentralized fashion in subspaces. We
then present an isomorphism that imposes these desired conditions, particularly
on two-time-scale systems. Decentralized computations are performed in the
transformed coordinates, yielding a conservative approximation of the viability
kernel in the original state space. Significant reduction of complexity can be
achieved, allowing the previously inapplicable tools to be employed for
treatment of higher-dimensional systems. We show the results on two examples
including a 6D system.
