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Consider the system given by

`[[x_(1)^(?)],[x_(2)^(?)]]=[[0,1],[-6,-3]][[x_(1)],[x_(2)]]+[[0],[7]]u,;y=[[1,0]][[x_(1)],[x_(2)]]`

And has a performance index

`J=\int_0^(\infty ) (x^(TT)[[2,0],[0,1]]x+u^(T)u)dt,;R=1`

The requirement for the full-state feedback regulator system controller using LQR. Follows by: a) Find the controllability and observability of the system. (6 marks) b) Determine the gain K c) Determine the optimal matrix gain

`K_(LQR)`

. Note: Show calculation using manual and MATLAB.help