Additive state decomposition is like breaking down a big puzzle into smaller puzzles to understand it better. Imagine you have a big puzzle with 1000 pieces and you want to see what is inside. You may not be able to see all of the details when it's put together, so you start by taking it apart into smaller pieces. You may separate the edges and corners, then the blue and green pieces, and so on.
In the same way, additive state decomposition helps us understand complicated things by breaking them down into smaller, easier-to-understand parts. It's often used in science and technology to study how things work, such as how a car engine or computer program functions.
For example, let's say we're trying to understand how a person's voice changes when they speak. Instead of looking at the whole process at once, we might break it down into smaller parts: the brain processing the words, the vocal cords vibrating, the sounds traveling through the mouth and throat, and the air being pushed out of the lungs. By looking at these smaller "puzzles" and understanding how they fit together, we can better understand how a person's voice changes when they speak.
Additive state decomposition is a way to simplify complex systems by dividing them into smaller, more manageable parts. By understanding how each part works individually, we can gain insights into how the system as a whole functions.