Laplace in Matrices step by step

Hello,

I have a question about calculating with matrices. So, my problem is: I have these matrices of state space model: A=[-5 1 3; 4 -4 1; 1 1 -6]; B=[1; 2; 3]; C=[3 2 4]; D=4; I=[1 0 0; 0 1 0; 0 0 1];

From these matrices I want to get transfer function.

I know that I can simply do it with use of SS like these: sys=SS(A,B,C,D) tf(sys) zpk(sys)

In my case I want to get solution by calculating these theoretical equation: G(s)=C((s*I-A)^-1)*B+D in Matlab I get an error because s is not defiend. How can I solve these problem, that I could solve these equation step by step? s is a Laplace operator ofc.

Thank you.

Answer 1

[Star Strider]

In your modern control textbook, it should mention that the inverse Laplace transform of the matrix defined by (s*I-A)^-1 is the matrix exponential, expm, specifically expm(A*t). I will let you take it from there. It should all be in your textbook.

You will need to create a for loop to simulate your system, because you have to solve it for each value of ‘t’, and create a result matrix with the appropriate dimensions to store the output of each step. Be certain to plot the result of your simulation so you can detect problems and see the successful results.