Question

The state space representation of the system is, egin{equation} dot{X} = egin{bmatrix} -1 & 0\ 0 & -3 end{bmatrix} X + egin{bmatrix} 1\ 1 end{bmatrix} u(t) end{equation} y = egin{bmatrix} 1 & -1 end{bmatrix} X The transfer function of the system is, (a) frac{s+1}{s^2+4s+3} (b) frac{2}{s^2+4s+3} (c) frac{s}{s^2+4s+3} (d) frac{s+3}{s^2+4s+3}

          The state space representation of the system is,
egin{equation*}
dot{X} = egin{bmatrix} -1 & 0\ 0 & -3 end{bmatrix} X + egin{bmatrix} 1\ 1 end{bmatrix} u(t)
end{equation*}
y = egin{bmatrix} 1 & -1 end{bmatrix} X
The transfer function of the system is,
(a) frac{s+1}{s^2+4s+3}
(b) frac{2}{s^2+4s+3}
(c) frac{s}{s^2+4s+3}
(d) frac{s+3}{s^2+4s+3}

$The state space representation of the system is, eginequation* dotX = eginbmatrix -1 0 0 -3 endbmatrix X + eginbmatrix 1 1 endbmatrix u(t) endequation* y = eginbmatrix 1 -1 endbmatrix X The transfer function of the system is, (a) fracs+1s^2+4s+3 (b) frac2s^2+4s+3 (c) fracss^2+4s+3 (d) fracs+3s^2+4s+3$

Added by Amanda M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

07/05/2023

Step 1

(a) s2+4s+3 = 5+1 = 6 Show more…

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The state space representation of the system is: X_dot = [[-1, 0], [0, -3]]X + [[1], [1]]u(t) y = [1, -1]X The transfer function of the system is: (a) (s + 1) / (s^2 + 4s + 3) (b) 2 / (s^2 + 4s + 3) (c) s / (s^2 + 4s + 3) (d) (s + 3) / (s^2 + 4s + 3)