GO Electrical
0 votes

The state variable description of an LTI system is given by

$$\begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 & a_1 & 0 \\ 0 & 0 & a_2 \\ a_3 & 0 & 0 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} + \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} u $$ $$y=\begin{pmatrix} 1 & 0 & 0 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix}$$

where $y$ is the output and $u$ is the input. The system is controllable for

  1. $a_1 \neq 0, \: a_2=0, \: a_3 \neq 0$
  2. $a_1 = 0, \: a_2 \neq 0, \: a_3 \neq 0$
  3. $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$
  4. $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
in new by (1.4k points)
recategorized by

Please log in or register to answer this question.

Answer:
Welcome to GATE Overflow, Electrical, where you can ask questions and receive answers from other members of the community.

847 questions
37 answers
10 comments
26,100 users