According to my book, given a MIMO system with n inputs and m outputs (corresponding to the n inputs), the model itself is said to be time-invariant if a time shifting of inputs causes a time shifting of outputs. Anyway I am not sure if each output is a function of only one input or not because of "corresponding to the n inputs".
2026-04-06 04:16:47.1775449007
Time-invariance of a MIMO system
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A system is (regardless of the amount of inputs / outputs) time-invariant if applying the same input to the same initial state at time $t$ yields the same response if it is applied at time $t+\tau$. This means that if I push a cart right now, its response should be the same as if I push this cart an hour from now, and the same a day from now and so on. Nothing changes if the same input is applied at a different time, as such its a time-invariant system. an example of a time-variant system could be a leaf spring that looses tension over time due to wear and corrosion. As the response at time $t=0$ (when it has just been made) and $t = \tau$ (a large time of doing nothing) alters.