  Dynamical systems with prescribed-time convergence sometimes feature a
right-hand side exhibiting a singularity at the prescribed convergence time
instant. In an open neighborhood of this singularity, classical absolutely
continuous Filippov solutions may fail to exist, preventing indefinite
continuation of such solutions. This note introduces a generalized Filippov
solution definition based on the notion of generalized absolute continuity in
the restricted sense. Conditions for the continuability of such generalized
solutions are presented and it is shown, in particular, that generalized
Filippov solutions of systems with an equilibrium that is attractive, in
prescribed time or otherwise, can always be continued indefinitely. The results
are demonstrated by applying them to a prescribed-time controller for a
perturbed second-order integrator chain.
