Use MatLab to convert from state space to state space (symbolic)

This script requires the MatLab's symbolic toolbox

% Start by clearing everything
clear all
clc
format compact

Declare all symbolic variables

syms k1 k2 b m

Define state space system

A=[0 1 0; -(k1+k2)/m 0 k1/m; k1/b 0 -k1/b];
B=[0; 1/m; 0];
C=[0 0 1];
D=0;

Define state transformation matrix and find its inverse

T=[1/2 0 1/2; -1 0 1; 0 1 0;];
Tinv=inv(T)

Tinv =
    1.0000   -0.5000         0
         0         0    1.0000
    1.0000    0.5000         0

Find new state space system

% Ahat
Ahat = simplify(T*A*Tinv)

% Bhat
Bhat = T*B

% Chat
Chat = C*Tinv

% Dhat
Dhat = D

Ahat =
[     0,         -k1/(2*b), 1/2]
[     0,             -k1/b,  -1]
[ -k2/m, (2*k1 + k2)/(2*m),   0]
Bhat =
   0
   0
 1/m
Chat =
    1.0000    0.5000         0
Dhat =
     0