Hi folks, can anyone think of an example of a first order system that yields an unstable zero input response? I would argue that the inverted pendulum does not, because that system is only unstable with an mg input and I'm only interested in zero input response. Does this not exist?


More: A zero-input response (by definition) is the response of a system that DOES have energy from initial conditions, just no input. So I believe it can grow unbounded due to the initial stored energy in the system. I just can't think of a physical example to illustrate this.