How to find the derivative of this Lyapunov function?

Hello!

I want to find the derivative of this Lyapunov function with respect to the differentiation parameters e, ΔKx, ΔKr.

where ΔKx = Kx_hat - Kx and ΔKr = Kr_hat - Kr , that is

Thanks in advance!

[RoBoTBoY]

I tried that, but without results.

Kx = sym('Kx');
Kr = sym('Kr');
Kx_hat = sym('Kx_hat');
Kr_hat = sym('Kr_hat');
gamma_x = sym('gamma_x');
gamma_r = sym('gamma_r');
Lambda = sym('Lambda');
e = sym('e');
P = sym('P');

DKx = Kx_hat - Kx;
DKr = Kr_hat - Kr;
V = e'*P*e + trace(DKx'*(gamma_x^-1)*DKx*abs(Lambda)) + trace(DKr'*(gamma_r^-1)*DKr*abs(Lambda));
diff_V = diff(V,e,DKx,DKr)

Answer 1

[Sulaymon Eshkabilov]

You have overlooked a couple of points

V does not contain Kx_hat,Kx, Kr_hat, Kr variables and thus, no need to introduce:

DKx = Kx_hat - Kx;

DKr = Kr_hat - Kr;

syms gamma_x  gamma_r  Lambda E P
syms DKx DKr
syms V(E, DKx, Dkr)

V = E'*P*E + trace(DKx'*(gamma_x^-1)*DKx*abs(Lambda)) + trace(DKr'*(gamma_r^-1)*DKr*abs(Lambda));
diff_V_e   = diff(V, E)
diff_V_DKx = diff(V,DKx)
diff_V_DKr = diff(V,DKr)

Good luck