Question

(b) A system is represented by a transfer function $G(s) = frac{Y(s)}{U(s)} = frac{1}{s^2 + 3s + 2}$. Determine i. a state-space representation for this system. ii. the impulse response of this system. iii. the solution $y(t)$ when the initial condition is given by $egin{bmatrix} y(0) dot{y}(0) end{bmatrix} = egin{bmatrix} 2 0 end{bmatrix}$. (c) The solution to a linear time-invariant system when the input $u(t) = tu_s(t)$ and zero initial condition ($y(0) = 0$) is given by $y(t) = (t - 1 + e^{-t})u_s(t)$. Find the impulse response and the transfer function of the system.

          (b) A system is represented by a transfer function $G(s) = frac{Y(s)}{U(s)} = frac{1}{s^2 + 3s + 2}$.
Determine
i. a state-space representation for this system.
ii. the impulse response of this system.
iii. the solution $y(t)$ when the initial condition is given by $egin{bmatrix} y(0)  dot{y}(0) end{bmatrix} = egin{bmatrix} 2  0 end{bmatrix}$.
(c) The solution to a linear time-invariant system when the input $u(t) = tu_s(t)$ and zero initial condition ($y(0) = 0$) is given by $y(t) = (t - 1 + e^{-t})u_s(t)$. Find the impulse response and the transfer function of the system.

$(b) A system is represented by a transfer function G(s) = fracY(s)U(s) = frac1s^2 + 3s + 2. Determine i. a state-space representation for this system. ii. the impulse response of this system. iii. the solution y(t) when the initial condition is given by eginbmatrix y(0) doty(0) endbmatrix = eginbmatrix 2 0 endbmatrix. (c) The solution to a linear time-invariant system when the input u(t) = tus(t) and zero initial condition (y(0) = 0) is given by y(t) = (t - 1 + e^-t)us(t). Find the impulse response and the transfer function of the system.$

Added by Patricia M.

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