function [Phi, Gamma] = c2d_ncs(a, b, deltat)
%C2D_NCS Converts a state space model in continuous time
% to a state space discrete time equivalent model.
% In MATLAB you use the function as follows:
% [Phi, Gamma] = ced_ncs(A,B,deltat)
% The output is the discrete equivalent of the continuous-time
% x = Ax + Bu
% i.e. the outputs are the matrices in the model:
% x = Phi(deltat) * x + Gamma(deltat) u
% k+1 k k
% where the assumption is made that the input is held constant over the
% sample time deltat.
[ma,na] = size(a);
[mb,nb] = size(b);
error('The matrix a must be square')
error('The matrix b must have the same number of rows as the matrix a')
% Have you done the exercise that asks you to verify the following?
augmented_matrix = [[a b];zeros(nb,na+nb)];
exp_aug = expm(augmented_matrix*deltat);
Phi = exp_aug( 1:na, 1:na );
Gamma = exp_aug( 1:na, na+1:na+nb );
% Do you understand this code?