Question

Problem 5: For the given difference equation of a dynamic system.

y k+2 +3y k+1 +2y k =u k+1 +3u k

please find its state space model.

answer:

Two models are given below. They are [ matrix x 1 |k+11\\ x 2 [k+1] matrix ]=[ matrix 0&-2\\ 1&-3 matrix ][ matrix x 1 |k|\\ x 2 |k| matrix ]+[ matrix 3\\ 1 matrix ] nu(k)

y[k]= 1 0&1 1 [ matrix x 1 [k]\\ x 2 [k] matrix ]

[ matrix x 1 [k+1]\\ x 2 [k+1] matrix ]=[ matrix -3&3\\ -2&0 matrix ][ matrix x 1 [k]\\ x 2 [k] matrix ]+[ matrix 1\\ 3 matrix ]v|k]

y[ kappa]=[1&0][ matrix x 1 [ matrix x 1 [ kappa]\\ x 2 [ kappa] matrix ]​

Answer 1

Answer:

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