%% Demonstration of stability of switched systems

%%
% Example 4.7 from (Lin & Antsaklis, 2022), page 177.

%% Unstable systems
% Matrices describing two unstable systems are
Aa = [1, -100; 10, 1]
Ab = [1, 10; -100, 1]

eig(Aa)
eig(Ab)

%% Plotting the vector fields

[X1,X2] = meshgrid(-10:2:10,-10:2:10);
Fa1 = Aa(1,1)*X1 + Aa(1,2)*X2;
Fa2 = Aa(2,1)*X1 + Aa(2,2)*X2;

figure(1)
quiver(X1,X2,Fa1,Fa2)
axis equal

Fb1 = Ab(1,1)*X1 + Ab(1,2)*X2;
Fb2 = Ab(2,1)*X1 + Ab(2,2)*X2;

figure(2)
quiver(X1,X2,Fb1,Fb2)
axis equal

%% Solving for the (stable) state responses of a switched system
% Again, the definition of the switched model, including the switching
% logic, is provided in the equally named file.
sbu = SwitchBetweenUnstable();

% Initial conditions
x0 = [1; 1];
q0 = 1;

% Time spans
tspan = [0, 1];
jspan = [0, 30];

% Specify solver options.
config = HybridSolverConfig('AbsTol', 1e-3, 'RelTol', 1e-7);

% Compute solution
sol = sbu.solve([x0;q0], tspan, jspan, config);

%% Plotting the solution of a switched system
figure(3)
%plotFlows(sol)
%plotHybrid(sol)
hp = HybridPlotBuilder().plotPhase(sol.select([1,2]))
hold on
axis equal
x1 = (-2:2);
plot(x1,-x1)
plot(x1,zeros(length(x1)))
grid on
hold off