Initial conditions for systems described in state space - LTI or not?

1. Do LTI systems have initial conditions?
2. Is state-space LTI?
3. Why are initial conditions zero for a LTI system?
4. Which response of LTI system does not depend on initial conditions?

Do LTI systems have initial conditions?

A causal LTI system has zero initial conditions and impulse response ℎ(𝑡). Its input (𝑡) and output (𝑡) are related through the linear constant-coefficient differential equation. d 2 y ( t ) d t 2 + α d y ( t ) d t + α 2 y ( t ) = x ( t ) .

Is state-space LTI?

Linear Time Invariant (LTI) state space models are a linear representation of a dynamic system in either discrete or continuous time. Putting a model into state space form is the basis for many methods in process dynamics and control analysis.

Why are initial conditions zero for a LTI system?

We use LTI systems in practice. That means the system should be LINEAR. Zero initial conditions ensure Linearity. That is why, Initial Conditions are assumed to be Zero in transfer function model.

Which response of LTI system does not depend on initial conditions?

Explanation: A LTI system is said to be memoryless only if it does not depend on any previous value of the input.