>>11979374*Regulate and track a set point: So you have a system, usually a dynamical system hence the differential equation, and you want it to behave in a certain way.
Example would be a robot manipulator, that thing has certain dynamic behaviors that are described by the differential equations obtained from an Euler Lagrange model, you want the end-effector to track a trajectory or regulate itself at some fixed point, you inject an input (with feedback, aka with measurements of the output positions and velocities for example) that will shape the dynamics of the robot so it tracks the desired trajectory or fixed point.
Linear design is pretty straight forward and uses Laplace domain and Linear algebra.
Non linear stuff uses Lyapunov and Lyapunov-like theorems.
Another thing that is very important in control is stabilizing equilibrum points of system. For example, the cart-pendulum's pendulum up equilibrium point is an unstable one. You can input a control law so the equilibrium becomes an stable one.
The most important concept in control is stability, so I suppose that there are some models in physics that are described by unstable differential equations that could somehow be stabilized?
