Frequency response of marginally stable LTI systems

1. What is frequency response of LTI system?
2. What is a marginally stable system?
3. How do you tell if a system is stable marginally stable or unstable?
4. What is the consequence of marginally stable systems?

What is frequency response of LTI system?

The frequency response of the system, from the definition in Equation (12.11), is thus. −jΩ −j2Ω H(Ω) = h[0] + h[1]e + h[2]e .

What is a marginally stable system?

A marginally stable system is one that, if given an impulse of finite magnitude as input, will not "blow up" and give an unbounded output, but neither will the output return to zero. A bounded offset or oscillations in the output will persist indefinitely, and so there will in general be no final steady-state output.

How do you tell if a system is stable marginally stable or unstable?

If the system is stable by producing an output signal with constant amplitude and constant frequency of oscillations for bounded input, then it is known as marginally stable system. The open loop control system is marginally stable if any two poles of the open loop transfer function is present on the imaginary axis.

What is the consequence of marginally stable systems?

Even if we have a bounded input as n tends to inf, we will have an bounded output. Hence, the system resolves to be a stable one. What is the consequence of marginally stable systems? The system will be a purely oscillatory system with no damping involved.