GATE EE 2016 Question Paper (06-Feb-2016) (Shift 2)

Consider the following state-space representation of a linear time-invariant system.

x≤ft( t ) = ≤ft[ {*20c 1&0\\ 0&2 } ]x≤ft( t ),y≤ft( t ) = c^Tx≤ft( t ),c = ≤ft[ {*20c 1\\ 1 } ]and x≤ft( 0 ) = ≤ft[ {*20c 1\\ 1 } ]

The value of $y\left(t\right)$ for $t={\log }_{\mathrm{e}}2$ is __________.

Loop transfer function of a feedback system is $G\left(s\right)H\left(s\right)=\frac{s+3}{s^2\left(s-3\right)}.$ Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of G(s) H(s) encircles $-1+j0$

Given the following polynomial equation

$s^3+5.5s^2+8.5s+3=0,$

the number of roots of the polynomial, which have real parts strictly less than $-1$, is ________

Suppose $x_1\left(t\right)$ and $x_2\left(t\right)$ have the Fourier transforms as shown below.



Which one of the following statements is TRUE?

The output of a continuous-time, linear time-invariant system is denoted by $T\left\{x\left(t\right)\right\}$ where $x\left(t\right)$ is the input signal. A signal $z\left(t\right)$ is called eigen-signal of the system , when $T\left\{z\left(t\right)\right\}=\gamma z\left(t\right)$, where $\gamma$ is a complex number, in general, and is called an eigenvalue of $T$. Suppose the impulse response of the system $T$ is real and even. Which of the following statements is TRUE?