%% Use MatLab to convert between state space representations
% This script requires the MatLab's symbolic toolbox

% Start by clearing everything
clear all
clc

%%
% Declare all symbolic variables
syms a1 a2 a3 a4 b0

%%
% Define state space system
A=[0 1 0 0; 0 0 1 0; 0 0 0 1; -a4 -a3 -a2 -a1];
B=[0; 0; 0; b0;];
C=[1 0 0 0];
D=0;

% Define transition matrix
R=[0.5 0.5 0 0; -0.5 0.5 0 0; 0 0 1 0; 0 0 0 1];

%Find new state space representation
Anew=inv(R)*A*R
Bnew=inv(R)*B
Cnew=C*R
Dnew=D
