Why is it necessary to know a state of a system?
If the system has memory, you need to know what state the memory is in. For example: a system with a low pass filter of a resistor and a capacitor will respond differently if the capacitor is fully charged or if the capacitor starts with zero voltage. The system will respond differently depending on the initial conditions or state

It isn't simply enough to know how a system will respond, but you also need to know what state it is in now to determine it's future behavior 

Another example of this is useful for analyzing the circuit. If you zero out the state and only consider the input this is called "Zero-State" analysis. 
Conversely, if you zero out the input and supply a state, it's called "Zero-Input" analysis. 


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