“How can we modify a state-space to become more stable?”
State-spaces are often used in control system design to represent a plant. However, sometimes the system by itself is unstable. So how can we use our engineering mindset to solve this? Well, what we can do is introduce an extra feedback loop with some constants that modify the poles of the system such that they are all in the right-half plane. This is known as Pole Placement and is one of the most commonly used techniques in classical control.
Image credit http://ctms.engin.umich.edu