If the impulse response of a causal LTIC system is $h(t) = \delta(t) + \sin(t)u(t)$, is it marginally stable or unstable (BIBO)?

If you take the $$H(s) = \mathcal{L}[h(t)]$$ the poles are on the imaginary axis so the system should be marginally stable, but is it?

• The system is supposed to be causal so $h(t) = 0, \forall t < 0$. So yes, I meant $sin(t)u(t)$, sorry. Dec 16, 2020 at 7:26
• Okay, thanks for clarifying. Dec 16, 2020 at 10:52