# Multiplication Of Control System Polynomes In MatLab®

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The reduction of sets of polynomials into one transfer function of a system is a very important work in control systems engineering. Matlab® provides various kinds of commands for this. One of these commands is the ‘conv()’ command.

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Here we show you how to use the ‘conv()’ command to multiplicate the polynomials in Matlab®.

## Use Of The ‘conv()’ Command In MatLab® For Transfer Functions

There can be different polynomials in closed-loop or open-loop control systems to be multiplicated. Consider a situation that we have two polynomials in s-domain like them;

x = 3s^2+5s-3;

y = 2s^3+2s+1;

Take a look at the very basic code below;

``````>> x = [0 3 5 -3];
y = [2 0 2 1];
z = conv(x,y)

z =

0     6    10     0    13    -1    -3

>> ``````

In this example, we defined two variables ‘x’ and ‘y’ which include the coefficients of the polynomials in the s-domain. And we typed these variables inside the ‘conv()’ command to get the result.

The result includes the coefficients of the multiplication of the s-domain polynomials. As you understand that, the ‘conv()’ command is a very important command for the reductions of closed-loops or open-loops.

## Conclusion

The use of the ‘conv()’ command in Matlab® for the reduction of control systems is very simple like above.

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