An active one-port network question

I want to check if an active one-port network is stable or not under the condition of terminating with a certain passive element at the port.

Now, I can write the input impedance of this one-port network. So If I give such network a voltage excitation, I can calculate the response current flowing into the network. From the analytic expression of this response, I know all its poles are in left half s-plane. So I know this response is stable.

My question is: based on such stable response, can I make the conclusion that all the responses at any nodal inside the network are stable?

I know when people check stability, like feedback amplifier, they use transfer function. But no one calculate the response at all the nodal in a network. So I doubt what they do guarantee the stability. However, I can prove it. I need your help.

Thanks.