MRPI_Par.m

%% Maximal RPI Set Computation for parametric uncertainty 
% Monimoy Bujarbaruah


function P = MRPI_Par(mat_set, X, U,  W)

    % computation of a robust invariant set for given LTImodel.  
    maxIterations = 100;
    X0 = X;                                                            % initial set constraint

    for j = 1:maxIterations
        % subtract noise    
        S = X0 - W;
        for i = 1: size(mat_set,3)  % for ALL models 
            model = LTISystem('A',mat_set(:,:,i)); 
            % backward reachable set
            Rm(i) = model.reachableSet('X', S, 'U', U,...
                             'direction', 'backward');
        end
        R = Rm(1); 

        for i = 2:size(mat_set,3)
            R = intersect(R,Rm(i));                                    % take COMMON parts
        end

        % intersect with the state constraints
        P = R.intersect(X0);
        if P==X0
            break
        else
            X0 = P;
        end
    end
    
end