function p1b
% Simulation of a circuit with two capacitors, change of ss variables
% Feb 2016, J. Gaspar

R= 1e3;
C= 1e-3;

A= [-1 1; 1 -2]/(R*C);
B= [1/C 0]';
C= [0 1]; % note this overwrites C
D= 0;

[y,t]= step(ss(A,B,C,D));

figure(201); clf
plot(t,y,'.-')

for i=1:100
    M= mk_rank2_random_matrix;

    A2= M*A*inv(M);
    B2= M*B;
    C2= C*inv(M);
    D2= D;
    
    [y,t]= step(ss(A2,B2,C2,D2));

    hold on
    plot(t,y,'o')
    hold off
    title(sprintf('experiment %d',i))
    drawnow
end
legend('default ss vars', 'modified ss vars')


function M= mk_rank2_random_matrix
while 1
    M= rand(2,2);
    if rank(M)==2
        return;
    end
end
