riccati_cost_functional.m

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function [J, lQ] = riccati_cost_functional(model, model_data, sim)
%[J,lQ] = riccati_cost_functional(model, model_data, sim)
%
%  Evaluate the cost functional for the model and for the feedback
%  information stored in the simulation structure sim.
%
%  This is done by solving a low rank Lyapunov equation:
%    Y' X E + E' X Y = C' C + E' P B B' P E
%  where Y = A - B B' P E.
% 
% Andreas Schmidt, 2015
[E,A,B,C,x0] = riccati_assemble_system_matrices(model, model_data);
Z = sim.Z;

Y = A - B*(B'*Z)*(Z'*E);
lG = [C; B'*Z*(Z'*E)];
lQ = lyap_sgn_fac(Y, lG, E);
J = (lQ*(E*x0))'*(lQ*(E*x0));

end