Extending the concept of linearization to dynamic systems, you can write continuous-time
nonlinear differential equations in this form:x ̇(t) =fx(t),u(t),t
y(t) =gx(t),u(t),t.In these equations, x(t) represents the system states, u(t) represents the inputs to the
system, and y(t) represents the outputs of the system.A linearized model of this system is valid in a small region around the operating point
t=t 0 , x(t 0 )=x 0 , u(t 0 )=u 0 , and y(t 0 )=g(x 0 ,u 0 ,t 0 )=y 0.To represent the linearized model, define new variables centered about the operating
point:2 Linearization