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the difference equation y(+2)-(n+1)-(n)=x(n). -{(?). (n)= n≥o n20 and initial conditions (0)=0, y1)=1 n<0 Applying the z-transform to both sides of the equation find the expression for Y(z) Using the fractional representation of Y(z) find the original sequence (n) Determine whether the discrete control system described by the equation above is stable or unstable

the difference equation y(+2)-(n+1)-(n)=x(n). -{(?). (n)= n≥o n20 and initial conditions (0)=0, y1)=1 n<0 Applying the z-transform to both sides of the equation find the expression for Y(z) Using the fractional representation of Y(z) find the original sequence (n) Determine whether the discrete control system described by the equation above is stable or unstable

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Fig. 2 y(n+2)-(n+1)-(n)= x(n). the difference equation > (n)=< and initial conditions (0)=0, y(1)=1 n<0 Applying the z-transform to both sides of the equation find the expression for Y(2) n≥0 n20 Using the fractional representation of Y(z) find the original sequence (n) Determine whether the discrete control system described by the equation above is stable or unstable
Transcribed Image Text:Fig. 2 y(n+2)-(n+1)-(n)= x(n). the difference equation > (n)=< and initial conditions (0)=0, y(1)=1 n<0 Applying the z-transform to both sides of the equation find the expression for Y(2) n≥0 n20 Using the fractional representation of Y(z) find the original sequence (n) Determine whether the discrete control system described by the equation above is stable or unstable
Expert Solution
Step 1

The difference equation given is as follows:

yn+2-16yn+1-16yn=xn,  n≥0

With,

xn=12n,  n≥00,  n<0

and initial conditions  y0=0,  y1=1

(a) We will apply the Z-transform on the given difference equation.

z2yz-y0z2-y1z-16zyz-y0z-16yz=xzz2yz-z-16zyz-16yz=xzyzz2-z6-16-z=xz

yz6z2-z-16=z+xz......................................................................(1)

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