Program for Impulsive Difference Equations

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Write a MATLAB program to simulate the following impulsive difference equation
where , , , and , for
(a) Find values of y[n] (b) plot the solutions over the range, 1= n = 10.
  2 Comments
Jon
Jon on 19 Aug 2019
What have you tried to do so far? What problems have you encountered? Please include your code using the code button on the MATLAB answers toolbar.
Gokula Nanda
Gokula Nanda on 20 Aug 2019
I am acquainted with the solution of difference equations. But no idea, how can i program the equations with impulse?

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Accepted Answer

Jon
Jon on 20 Aug 2019
One way to approach this is to transform your difference equation in the single variable y to a system of two difference equations, which you can simply march forward in time.
So neglecting, for the moment the special condition when n = mk, you could define y1(n) = y(n) and y2(n) = y1(n-1), noting also that a(n), b(n) and c(n) are in fact not functions of n, but simple constants, and substituting for h(u) would give the system of equations
y1(n+1) = a*y1(n) - b*y2(n) - c*y2(n)^3
y2(n+1) = y1(n)
Assuming you have initial conditions for y you could then just march forward in a loop
a = -3/2
b = 1
c = 1/4
% assign initial conditions
y1(1)= y1ic % initial condition y for n=1
y2(1)= y2ic % initial condition y for n=0
% assign maximum iteration
nFinal = 11
% loop to march forward
preallocate
y1 = zeros(nFinal+1,1)
y2 = zeros(nFinal+1,1)
for n = 1:nFinal
y1(n+1) = a*y1(n) - b*y2(n) - c*y2(n)^3
y2(n+1) = y1(n)
end
% plot results (note y1 = y the variable you are interested in)
plot(y1) % with only one argument the x axis will just be the value of n
You will have to further modify your code to handle the special condition where n = m*k. I actually can't understand the details of what your are doing there from the description, for example I don't see where I_k is defined.
Hopefully this gives you a start on how to approach this.
  4 Comments
Jon
Jon on 21 Aug 2019
Your welcome. Glad to hear this worked. Good luck with your project

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