A discrete time system is stable if the roots of the characteristic equation are: In the left half of z-plane In the upper half of z-plane. Outside the unit circle centered at origin in the z-plane O Inside the unit circle centered at origin in the z-plane

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A discrete time system is stable if the roots of the characteristic equation
are:
In the left half of z-plane
In the upper half of z-plane.
Outside the unit circle centered at origin in the z-plane
Inside the unit circle centered at origin in the z-plane
Consider the system output Y(z) given by
0.3678z + 0.2644
Y(z) = K
z? – 1.3678z + 0.3678
The values v(kT) at the first two sampling instants are:
y(0) =0; y(T)= -1.3678
y(0) =0; y(T)= 0.3678
y(0) =0.3678; y(T)= 0.2644
O y(0) =0.3678; y(T)= 0
Transcribed Image Text:A discrete time system is stable if the roots of the characteristic equation are: In the left half of z-plane In the upper half of z-plane. Outside the unit circle centered at origin in the z-plane Inside the unit circle centered at origin in the z-plane Consider the system output Y(z) given by 0.3678z + 0.2644 Y(z) = K z? – 1.3678z + 0.3678 The values v(kT) at the first two sampling instants are: y(0) =0; y(T)= -1.3678 y(0) =0; y(T)= 0.3678 y(0) =0.3678; y(T)= 0.2644 O y(0) =0.3678; y(T)= 0
Consider a discrete time system with the closed-loop pulse transfer
function T(z) = K
22+3z+1
z2+0.9z+0.2
This system is:
Stable for all finite K.
Unstable for 0.7< k < *
O Unstable for all finite K
None of the above
Transcribed Image Text:Consider a discrete time system with the closed-loop pulse transfer function T(z) = K 22+3z+1 z2+0.9z+0.2 This system is: Stable for all finite K. Unstable for 0.7< k < * O Unstable for all finite K None of the above
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