I need to find a differential equation $x'=f(x)$ that has three equilibrium points that are


all sinks;
all sources.


So two differential equations total. Help!


Question: Stopping a DC motor using an H-bridge: forward+backward vs. 'brake'
Answer: Assuming you can measure the actual motor position, juggling forward and backward directions will be better in terms of stopping at the right place - use the position error to control the ratio of forward to reverse drive.

This does involve a lot of switching noise and high currents during deceleration : you may wish to employ resistive braking to lose most of the motor's speed, then switch to active drive to the final position.