## Find State Space Representation of Linearized non-linear System to find State Space Representation in Canonical form MATLAB

I have the following non-linear system and accompanying ODE:

I have the following ODE45 solution:

fun = @(t,X)odefun(X,K,C,M,F(t),resSize);

[t_ode,X_answer] = ode45(fun,tspan,X_0);

The input matrices are stiffness K(X), damping C mass M, and force F. resSize is the total number of masses in the system. To find the solution indirectly I introduced a change of variables to reduce the non-linear ODE to a first order linear ODE.

I would like to find the state space (SS) representation of my linearized non-linear system and corresponding ODE. More specifically, I would like to find the SS matrices A,B,C,D. I did not explicitly perform the change of variables. Rather, MATLAB did it for me. The ultimate goal of finding the SS representation (matrices A,B,C,D) is to then be able to find the canonical form of the non-linear ODE. I’m not sure if this can be done with a transfer function estimate of my ODE45 solution or some other MATLAB tool.I have the following non-linear system and accompanying ODE:

I have the following ODE45 solution:

fun = @(t,X)odefun(X,K,C,M,F(t),resSize);

[t_ode,X_answer] = ode45(fun,tspan,X_0);

The input matrices are stiffness K(X), damping C mass M, and force F. resSize is the total number of masses in the system. To find the solution indirectly I introduced a change of variables to reduce the non-linear ODE to a first order linear ODE.

I would like to find the state space (SS) representation of my linearized non-linear system and corresponding ODE. More specifically, I would like to find the SS matrices A,B,C,D. I did not explicitly perform the change of variables. Rather, MATLAB did it for me. The ultimate goal of finding the SS representation (matrices A,B,C,D) is to then be able to find the canonical form of the non-linear ODE. I’m not sure if this can be done with a transfer function estimate of my ODE45 solution or some other MATLAB tool. I have the following non-linear system and accompanying ODE:

I have the following ODE45 solution:

fun = @(t,X)odefun(X,K,C,M,F(t),resSize);

[t_ode,X_answer] = ode45(fun,tspan,X_0);

The input matrices are stiffness K(X), damping C mass M, and force F. resSize is the total number of masses in the system. To find the solution indirectly I introduced a change of variables to reduce the non-linear ODE to a first order linear ODE.

I would like to find the state space (SS) representation of my linearized non-linear system and corresponding ODE. More specifically, I would like to find the SS matrices A,B,C,D. I did not explicitly perform the change of variables. Rather, MATLAB did it for me. The ultimate goal of finding the SS representation (matrices A,B,C,D) is to then be able to find the canonical form of the non-linear ODE. I’m not sure if this can be done with a transfer function estimate of my ODE45 solution or some other MATLAB tool. transfer function, nonlinear, ode45, ode, matlab function, system, model MATLAB Answers — New Questions