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design an input that would produce an output at tf (final time), of v1=1, v2=2, v3=3,

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design an input that would produce an output at tf (final time), of v1=1, v2=2, v3=3, ... and so on. Specifically, I would like to recommend the following. (1) Run this part (and the part for xf=0) with n=5 (keeping it simple and avoiding numerical issues). (2) Also, when simulating (i.e., to prove that the input generates the desired output), consider making the simulation time step to be much smaller (e.g., instead of 1/20 consider 1/1000). If you feel that the results are not accurate enough, feel free to make the time step even small. (3) Also, make the final time tf=2 (this will help curb computational errors due to very large exponents). Refer book :“Linear System Theory,” by Wilson J. Rugh, Second Edition, Prentice Hall, 1996. Refer chapter controllability and observability,chapter 9