%% simulateTimeDomain 

%  Evaluation of the auxiliary state equation exploiting block structuring of feedback matrices K_uni, K_lam and eigenvalues decomposition 

%

%  inputs: 

% Az: Decomposed state matrix \Lambda_n

% fe, yi: Associated inputs fe_n, yi_n

% T: Time step

% U, Uinv: Matrices U and U^{-1} from decomposition

%

%  outputs: 

% ybar_n: System states ybar_n[k]  

%

function [ybar_n] = simulateTimeDomain(Az,fe,yi,T, U, Uinv)

% number of eigenvalues Q_n and time duration t_dur

Mu = size(Az,1);

dur = size(fe,2);

% define auxiliary system states 

uybar = zeros(Mu,size(fe,2));

% create a single input from fe and yi 

yi_time = zeros(Mu, size(fe,2));

yi_time(:,1) = yi;

excite = fe + yi_time;

uexcite = Uinv*excite;

% evaluate individual lines of auxiliary state equation

for mu = 1:Mu

    % evaluate individual lines by first-order filters

    uybar(mu,:) = filter(1,[1, -Az(mu,mu)],T*uexcite(mu,:));

end

% convert auxiliary states to desired system states ybar_n

ybar_n = U*uybar;

Published with MATLAB® R2019a