Floating Point scalar error while trying to find Grammians

This is my code, I'm trying to find the controllability and observability Grammians of the following system where k is unknown. Since i have k, i can't use the function gram(sys,'c'). So i'm trying to use the Grammian equation but i keep getting these errors:

Error using integral (line 85)

A and B must be floating-point scalars.

Error in control (line 15)

Wc = integral(fun,0,T)

Can anyone help me with this please?

syms k tau T

A = [0 1 0; 0 0 1; -6.63*k -171 -101.71];

B = [0;0;6.63*k];

C = [1 0 0];

D = 0;

A_T = A.';

B_T = B.';

C_T = C.';

fun =@(tau) expm(-A*taw).* B .* B_T .* expm(-A_T*taw);

Wc = integral(fun,0,T)

det_Wc = det(Wc)

fun1 = @(tau) expm(A_T*taw) .* C_T .* C .* expm(A*taw);

Wo = integral(fun1,0,T)

det_Wo = det(Wo)

Answer 1

[Shraddha Jain]

Hi Hussain,

You are experiencing this error because k is undefined, as a result, A and B are computed as symbolic variables and not matrices as expected by the function expm.