State diagram of a system is shown below. A system is described by the state variable equations \stackrel{˙}{X} = AX + BU\:;Y = CX + DU State variable equation of the system shown in figure above are

Correct Answer is : X=[−101−1]X+[−11]U Y=[1−1]X+U

{X}=\left[\begin{array}{cc}-1 & 0 \ 1 & -1]\end{array} X+\left[\begin{array}{c}-1 \ 1]\end{array} U Y=\left[\begin{array}{cc}1 & -1]\end{array} X+U

˙{X}=\left[\begin{array}{cc}-1 & 0 \ -1 & -1]\end{array} X+\left[\begin{array}{c}-1 \ 1]\end{array} U Y=\left[\begin{array}{cc}-1 & -1]\end{array} X+U

˙{X}=\left[\begin{array}{cc}-1 & 0 \ -1 & -1]\end{array} X+\left[\begin{array}{c}-1 \ 1]\end{array} U Y=\left[\begin{array}{cc}1 & -1]\end{array} X+U

˙{X}=\left[\begin{array}{cc}-1 & -1 \ 0 & -1]\end{array} X+\left[\begin{array}{c}-1 \ 1]\end{array} U Y=\left[\begin{array}{cc}-1 & -1]\end{array} X-U

GATE Electronics and Communications (EC) 2013 Solved Paper

Question : 64 of 65

Marks: +1, -0

State diagram of a system is shown below. A system is described by the state variable equations

\;{X}↖{˙} = AX + BU\:;Y = CX + DU

State variable equation of the system shown in figure above are

${X}={[\table -1 , 0 ; 1 , -1]} X+{[\table -1 ; 1]} U$
$Y={[\table 1 , -1]} X+U$
$˙{X}={[\table -1 , 0 ; -1 , -1]} X+{[\table -1 ; 1]} U$
$Y={[\table -1 , -1]} X+U$
$˙{X}={[\table -1 , 0 ; -1 , -1]} X+{[\table -1 ; 1]} U$
$Y={[\table 1 , -1]} X+U$
$˙{X}={[\table -1 , -1 ; 0 , -1]} X+{[\table -1 ; 1]} U$
$Y={[\table -1 , -1]} X-U$

Validate

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