As I know it depends if the state variable can be replaced with nonlinear combination of other state variables through solving nonlinear algebraic equations in order to make all new state variables in the following sort (or similar to that) or not:

x1_dot = x2;

x2_dot = x3;

...

xn_dot = f(x1, x2, ..., xn) 

So the answer is : not always possible.

The formal way would be to linearize the system around a equilibrium point (!)

1) To find a equilibrium point set all derivatives to zero and solve the set of nonlinear equations; 

then

2) To linearize the non-linear system use the Jacobian, i.e.

A=[dfi/dxj] , i=1,2...,n  d:denotes the partial deriv.; f1,f2,..fn: the nonlinear equations; x1,x2,..xn: your states.

B=[dfi/dui], ui: i-th input signal

* In matlab you can use a S-function to write your nonlinear system equations and then the commands:

eq_point=trim('  ') : to find equilibrium points

[A,B,C,D]=linmod('   ', eq_point): to linearize your system

(see more in any control book and Matlab help)

I think Siti meant nonlinear canonical form, rather than linearized one. Right? 

The best book on the subject is Isidori's  work.  There was feedback linearization, observers with linear error dynamics, and zero dynamics topics for SISO nonlinear systems.  Read Appendix A, Chapters 1 and 4 to get started.  

Please, see the paper in the journal

Automation and Remote Control, 2010, #5, 951-960.

State space equation can be converted to CCF by using Taylor series expansion and formation of state transition matrix.The resultant vector matrix equation involves state variable and control variable. The similar approach is followed in case of Kalman filter.