  The property that every control system should posses is stability, which
translates into safety in real-life applications. A central tool in systems
theory for synthesizing control laws that achieve stability are control
Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting
closed-loop state trajectory is contained within a cone with a fixed,
predefined shape, and which is centered at and converges to a desired
converging point. However, such a requirement often proves to be
overconservative, which is why most of the real-time controllers do not have a
stability guarantee. Recently, a novel idea that improves the design of CLFs in
terms of flexibility was proposed. The focus of this new approach is on the
design of optimization problems that allow certain parameters that define a
cone associated with a standard CLF to be decision variables. In this way
non-monotonicity of the CLF is explicitly linked with a decision variable that
can be optimized on-line. Conservativeness is significantly reduced compared to
classical CLFs, which makes \emph{flexible CLFs} more suitable for
stabilization of constrained discrete-time nonlinear systems and real-time
control. The purpose of this overview is to highlight the potential of flexible
CLFs for real-time control of fast mechatronic systems, with sampling periods
below one millisecond, which are widely employed in aerospace and automotive
applications.
