Where can I read up on zero state and zero input response for Discrete Time LTIs?

1. How do you find the zero-input response of LTI system?
2. How do you find the zero-input response from a transfer function?
3. Why does impulse response of LTI system take form of zero-input response?

How do you find the zero-input response of LTI system?

To find the zero input solution, take the Laplace Transform of the input with f(t)=0 and solve for X_zi(s). Note: since the initial condition was doubled, the zero input response was doubled.

How do you find the zero-input response from a transfer function?

Key Concept: The Zero Input Response and the Transfer Function. Given the transfer function of a system: The zero input response is found by first finding the system differential equation (with the input equal to zero), and then applying initial conditions.

Why does impulse response of LTI system take form of zero-input response?

is "no", because only a system with an input and an output can have an impulse response, a homogeneous ODE doesn't have an impulse response. The impulse response of a system, possibly described by an ODE, is the zero-state response to an input signal x(t)=δ(t).