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Lyapunov theory region of attraction

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Mo'ath Al-Hayek
Mo'ath Al-Hayek 2021-2-16
回答： Mo'ath Al-Hayek 2021-2-16
V (y) = y Py
I have to find the region of attraction for this lyaponov function so I wrote this code but I couldn't finish it. (( I want to change the values of c to find the best ROA)
clear all
A = [-11 1 ; 3 -1];
Q = eye(2);
P = lyap(A',Q);
p11= P(1,1)
p12 = P(1,2)
p22 = P(2,2)
x=[-2:0.005:2];
y=x;
[X,Y]=meshgrid(x,y);
Z = -((X.^2)+(Y.^2))-((2*p11*X)+(2*p12*Y)).*(6+X).*(X.^2);
c = 0;
X1 = [];
X2 = [];
for i=1:1:size(y,2)
for j=1:1:size(x,2)
if Z(i,j)>=(c-0.01) && Z(i,j)<=(c+0.01);
X1=[X1;x(j)];
X2=[X2;y(i)];
end
end
end
f =figure
subplot(2,2,1)
plot(X1,X2)
clear X Y x1 x2 x y Z
c = 0.1;
X = [];
Y = [];
for x1= -2:0.005:2;
Delta = (2*p12*x1)^2-4*p22*((p11*x1^2)-c);
if Delta>0
x21 = (-2*p12*x1-sqrt(Delta))/(2*p22);
x22 = (-2*p12*x1+sqrt(Delta))/(2*p22);
X = [X;x1;x1];
Y = [Y;x21;x22];
end
end
subplot(2,2,2)
plot(X,Y)
c = 0.008;
Z = [];
W = [];

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回答（1 个）

Mo'ath Al-Hayek
Mo'ath Al-Hayek 2021-2-16
The final result shall be approximate to this

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