Example of how to use ODE23 in MATLAB: make two files such as call_plant.m and plant.m as shown below, where plant is a simple double integrator.

At the MATLAB prompt, type: "call_plant"

% call_plant.m
x0 = [-1 2];
[T,x]=ode23('plant', [0 20], x0);

% plant.m
function [xdot] = plant(t,x)

xdot(1) = x(2);
xdot(2) = -1;
xdot = xdot';