  In applications, such as biomedicine and systems/synthetic biology, technical
limitations in actuation complicate implementation of time-varying control
signals. In order to alleviate some of these limitations, it may be desirable
to derive simple control policies, such as step functions with fixed magnitude
and length (or temporal pulses). In this technical note, we further develop a
recently proposed pulse-based solution to the convergence problem, i.e.,
minimizing the convergence time to the target exponentially stable equilibrium,
for monotone systems. In particular, we extend this solution to monotone
systems with parametric uncertainty. Our solutions also provide worst-case
estimates on convergence times. Furthermore, we indicate how our tools can be
used for a class of non-monotone systems, and more importantly how these tools
can be extended to other control problems. We illustrate our approach on
switching under parametric uncertainty and regulation around a saddle point
problems in a genetic toggle switch system.
