Define a polynomial in SOS

[Qu Cao]

I'm studying the problem of Lyapunov function in the discrete-time case.

For instance, the discrete-time system is

x1 (k+1) = x2(k)^2 + 3

x2 (k+1) = 2*x1(k)

Now I define a unknown polynomial as the Lyapunov function

[J(k), coef] = polynomial([x1 x2], 2);

So, how can I get the expression of J(k+1)? Can I use the subs function in MATLAB, something like

J(k+1) = subs(J(k), [x1 x2], [x2^2+3, 2*x1])

I think the type of J(k) is not symbolic any more. My problem is more complex than the example with more states and higher orders. Is there any way to perform substitution within the sdpvar?

[Johan Löfberg]

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