solve the riccati equations in matlab

Hi guys

I know how we can solve a Riccati equation in matlab. But this equation that I see in paper and named Riccati equation, it's not like them as it is:

S=A_k'*S*A_k+W-A_k'*S*B_k*inv(B_k'*S*B_k+U)*B_k'*S*A_k;

wher:

A=[-0.64 1.51 -22.95 9.78 0;-4.19 -20.63 9.93 0 0;0.68 -2.68 -1.04 0 0;0 1 0 0 0;0 0 1 0 0];

B=[-1.25 3.19;-109.84 1.98;-4.33 -20.17;0 0;0 0];

C=[0.04 0 0 0 0;0 1 0 0 0;0 0 1 0 0;0 0 0 1 0;0 0 0 0 1];

D=zeros(5,2);

sys = ss(A,B,C,D);

sysd = c2d(sys,10^-2);

A_k=sysd.A;

B_k=sysd.B;

C_k=sysd.C;

D_k=sysd.D;

U=[0.02 0.01;0.01 0.03];

W=[1 0.9 0.6 0.4 1;2 0.1 0.3 0.4 0.5;0.5 1 0.3 2 0.4;0.2 0.3 0.5 0.6 0.7;0.2 0.4 0.5 0.3 0.4];

Answer 1

[Roshni Garnayak]

You can use the following command to solve your equation:

[X,K,L] = idare(A,B,W,U,[],[]);

The equation provided in the documentation is:

The variables can be mapped as follows:

For further details, refer to the following link:

https://www.mathworks.com/help/control/ref/idare.html