The minimum potential energy of a system will be in the position of stable equilibrium.
In stable equilibrium, a system will return to its original position after being displaced from it. This is because the forces acting on the system will tend to restore it to its original position.
In unstable equilibrium, a system will move further away from its original position after being displaced from it. This is because the forces acting on the system will tend to move it away from its original position.
In neutral equilibrium, a system will neither return to its original position nor move further away from it after being displaced from it. This is because the forces acting on the system are balanced.
Therefore, the minimum potential energy of a system will be in the position of stable equilibrium.