. If there exists a continuously differentiable scalar function (known as a Lyapunov function candidate) such that: (Positive Definite) (Negative Semi-Definite) Then, the equilibrium point is stable. If
Once on the surface, the system is insensitive to matched uncertainties and perturbations. A common approach uses a switching control law, such as , to ensure C. Backstepping Design to ensure C. Backstepping Design ẋ2=f2(x1
ẋ2=f2(x1,x2)+g2(x1,x2)x3x dot sub 2 equals f sub 2 of open paren x sub 1 comma x sub 2 close paren plus g sub 2 of open paren x sub 1 comma x sub 2 close paren x sub 3 to ensure C. Backstepping Design ẋ2=f2(x1