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## Main Question or Discussion Point

Suppose that, I have a linear system which is analytically defined as below:

[itex]\frac{dx}{dt} = Ax + Bu \, .......... \, (I)[/itex]

[itex]y = Cx + Du \, ............ \, (II)[/itex]

I want to simulate this system in computer (not by using Matlab or any other libraries/tools) by sending input values and receiving corresponding output values. How do I do this? What is the basic idea?

Do I have to iterate the equation

What is

[itex]\frac{dx}{dt} = Ax + Bu \, .......... \, (I)[/itex]

[itex]y = Cx + Du \, ............ \, (II)[/itex]

*A*,*B*,*C*,*D*are matrices defining the system,*u*is input,*y*is output.I want to simulate this system in computer (not by using Matlab or any other libraries/tools) by sending input values and receiving corresponding output values. How do I do this? What is the basic idea?

Do I have to iterate the equation

*(I)*by calculating*dx/dt*and using it to calculate the value of*x*, then use it in equation*(II)*to find the output?What is

*x*vector for in the first place? Why do we calculate it?