Controller synthesis for a class of second-order nonlinear systems

This paper presents a constructive method to design stabilizing controllers for a class of second-order nonlinear systems whose input parts may vanish at the origin. A sufficient condition for the existence of control Lyapunov functions (CLFs) and stabilizing controllers is provided. In the case that the small control property does not hold, a formula for constructing continuous state feedback controllers to avoid extremely large control magnitude near the origin and to achieve ultimate boundedness is presented.