How can ı solve this difference equation ?

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FURKAN
FURKAN 2023-3-13
评论： FURKAN 2023-3-13
Consider the difference equation:
x(k + 2) - 1.3679x(k + 1) + 0.3679x(k) = 0.3679u(k + 1) + 0.2642u(k) where x(k) = 0 for k ≤0. The input u(k) is given by
u(k) = 0, k<0
u(0) = 1.5820
u(1) = -0.5820
u(k) = 0, k = 2,3,4,...
Determine the output x(k). Solve this problem both analytically and computationally with MATLAB

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采纳的回答

Torsten
Torsten 2023-3-13
编辑：Torsten 2023-3-13
Ran in:
um2 = 0;
um1 = 0;
u0 = 1.5820;
u1 = -0.5820;
u2 = 0;
xm2 = 0;
xm1 = 0;
x0 = 1.3679*xm1 - 0.3679*xm2 + 0.3679*um1 + 0.2642*um2
x0 = 0
x1 = 1.3679*x0 - 0.3679*xm1 + 0.3679*u0 + 0.2642*um1
x1 = 0.5820
x2 = 1.3679*x1 - 0.3679*x0 + 0.3679*u1 + 0.2642*u0
x2 = 1.0000
x3 = 1.3679*x2 - 0.3679*x1 + 0.3679*u2 + 0.2642*u1
x3 = 1.0000
So you have x2 and x3 and the formula for xk (k>=2) reads
x(k+2) - 1.3679*x(k+1) + 0.3679*x(k) = 0
Can you take it from here ?

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