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.
Tag: initial conditions
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.