Is there an alternative to lsim to calculate the forced response of a system?

Hello, I tried to use the lsim Matlab function in order to calculate the forced responses of a 2-DoF system. The problem is that these responses are wrong and I will explain why.

As you know, it is possible to write: {Y}=[H]{U} where {Y} is the responses vector, [H] the FRF of the system and {U} the input vector. This is what I made:

1. calculate {U} so that {Y} is a sinusoidal signal with amplitude equal to 5, then: {U}=[H]*{Y}, with [H]* pseudoinverse of [H] 2. tried to calculate {Y}=[H]{U} and it works 3. tried to calculate [Y,~,~]=lsim(my_sys,{D}) but the responses of my discrete state-space model, Y=[Y1 Y2] are not coherent with my first sinusoidal signal with amplitude equal to 5.

This is a brief (qualitative, not precise) description of what I did. Can you tell me if there is an alternative to the lsim command to evaluate the forced response of a MIMO discrete system?

[Milton]

If you could provide the code, then may understand your workflow precisely.

Using 'lsim', you need provide input history t,u, like lsim(sys,u,t).

I am not sure how you prepared 'my_sys' and {D}. And it seems 'my_sys' is discrete system. However, you mentioned [H] is FRF, which is frequency response function, and {U} ,{Y} should be in time domain.

How do you calculate {U} to ensure {Y}? Do you use State Space equation of MIMO system?