Converting a nonlinear state equation into state dependent matrix form

I have a set of nonlinear state equation with origin convergence. i want the representation in form [Xdot]= [A(x)] * [x]. I tried jacobian but it's not the accurate representation. Would appreciate any suggestion.

Answer 1

[Sam Chak]

Hi @Md Sabbir Haider

Based on your descriptions, it is entirely acceptable to use the nonlinear state equations for simulation purposes. If your manually-defined Jacobian representation yields inaccurate responses, it is possible that the linearization components have been calculated incorrectly.

%% nonlinear state equations
function dx = ode(t, x)
    dx(1)   =   x(2);
    dx(2)   = - x(2) - sin(x(1));
    dx      = [dx(1); 
               dx(2)];
end

%% simulation
[t, x]  = ode45(@ode, [0 10], [1 0]);
plot(t, x), grid on