How can i write this Lyapunov equation in Matlab?

Hello,

I would like to ask you how can i write this equation? I am new in Matlab, and i tried this code:

n = 100000;

x0 = 0.1;

step = 0.001;

e = exp(1);

a = [0.001 : step : 0.05];

a * e.^(n * lyap(a)) == abs(f.^n .* (x0 + a) - f.^n .* (x0));

e.^(n.* lyap(a)) == abs(f.^n .*(x0+a) - f.^n .* (x0));

lyap(a) == (1/n) .* ln((abs(f.^n * (x0+a) - f .^n * (x0))/a));

but i have this error:

>> Lyapunov

Error using lyap (line 23)

Not enough input arguments.

Error in Lyapunov (line 7)

a * e.^(n * lyap(a)) == abs(f.^n .* (x0 + a) - f.^n .* (x0));

Is it completely wrong or do i miss something?

Thank you!

Answer 1

[Shivang Srivastava]

Hi Eleni,

As per my understanding you are having trouble using lyap function. As the error suggest you have not sent sufficient parameters in lyap function.

X = lyap(A,Q)

This is the correct syntax for lyap function. You may refer to lyap documentation for more information.