how to create an discrete equation

my question is how to creat discrete equations, calculate them and put the created discrete equations in each other such that i get an final diskrete equation

For example:

I. y_1(k) = a*y_1(k-1)+b*x_1(k-1)

II. y_2(k) = c*y_2(k-1) + d*y_1(k-1)

Final equation: y_2(k) = c*y_2(k-1) + d*a*y_1(k-2) + d*b*x_1(k-2)

** The values of x_1, i can get from the data set x_1 and for k = 1, y_1(k-1) = 0

** I would like to realize it into "sym".

thank you in advance

[Rik]

What have you tried so far?

Answer 1

[Surya Talluri]

I understand that you want to create discrete functions using Symbolic Math Toolbox. You can implement it by creating symbolic functions x_1(k), y_1(k), y_2(k)

syms a b c d x_1(k) y_1(k) y_2(k)

y_1(k) = a*y_1(k-1)+b*x_1(k-1);
y_2(k) = c*y_2(k-1) + d*y_1(k-1);
  
y_2(k)
  
ans =

c*y_2(k - 1) + d*(a*y_1(k - 2) + b*x_1(k - 2))

For replacing x_1 values, you can use “subs” function.

You can refer to following documentation for further understanding:

• syms - https://www.mathworks.com/help/symbolic/syms.html
• symfun - https://www.mathworks.com/help/symbolic/symfun.html
• subs - https://www.mathworks.com/help/symbolic/subs.html