  Limitations to the speed of evolution of quantum systems, typically referred
to as quantum speed limits (QSLs), have important consequences for quantum
control problems. However, in its standard formulation, is not straightforward
to obtain meaningful QSL bounds for time-dependent Hamiltonians with unknown
control parameters. In this paper we present a short introductory overview of
quantum speed limit for unitary dynamics and its connection to quantum control.
We then analyze potential methods for obtaining new bounds on control times
inspired by the QSL. We finally extend the work in [Poggi, Lombardo and
Wisniacki EPL 104 40005 (2013)] by studying the properties and limitations of
these new bounds in the context of a driven two-level quantum system
