Simulating linear systems with non-zero initial conditions

I have discussed in another post how to work with state-space models to simulate the response of linear systems using Matlab’s lsim. It is however also possible to approach this problem from a transfer-function point of view without having to mess with state-space at all.

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Simulating linear systems with non-zero initial conditions in state space

Matlab’s lsim function for simulating linear systems will give you the option to provide an initial condition if your system is in state-space but not for transfer-functions.

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To disturb or not to disturb?

So here is a recurrent question. You have some model that has a constant showing up on the differential equation and you’re not sure how to handle it. For example, your model looks like:

$$\dot{y}(t)=ay(t)+bu(t)+c$$

where $c$ is a constant. There are multiple ways you can handle this situation.

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