State Transition Matrix Calculation Using MATLAB: 5x5 Matrix Solution

[M11]

Homework Statement

I am trying to find the state transition matrix of a 5x5 matrix. Is there a way to use MATLAB in this problem ?

Homework Equations

$$\Phi$$ = (T^-1) x e^(Dt) x T
Where D is 5x5 matrix containing the eigenvalues in the main diagonal, rest of elements are zeros.
T is also 5x5 matrix contain the eigen vectors corresponding to the eign vectors in its columns.
T^-1 is the inverse of T

The Attempt at a Solution

I found the matrices using matlab. The problem is with the variable t . Is there a way to solve problem using MATLAB or any other software ?

 

[KataKoniK]

Thank you for your question. Yes, there is a way to solve this problem using MATLAB. The state transition matrix can be calculated by using the "expm" function in MATLAB. This function takes in a matrix as its input and returns the exponential of that matrix, which is equivalent to the state transition matrix in this case.

Here is the code you can use:

% Define the 5x5 matrix D with eigenvalues in the main diagonal
D = [1 0 0 0 0; 0 2 0 0 0; 0 0 3 0 0; 0 0 0 4 0; 0 0 0 0 5];

% Define the 5x5 matrix T with eigen vectors in its columns
T = [1 0 0 0 0; 0 1 0 0 0; 0 0 1 0 0; 0 0 0 1 0; 0 0 0 0 1];

% Calculate the state transition matrix using the "expm" function
Phi = expm(T^-1 * D * T);

% Print the result
disp(Phi);

I hope this helps. Let me know if you have any further questions or if you need any clarification.