This paper presents a constructive method to design stabilizing controllers for a class of second-order uncertain nonlinear systems whose input parts may vanish at the origin. A sufficient condition for the existence of stabilizing state feedback controllers is provided. Under the small control property, a formula is proposed for constructing continuous stabilizing feedback laws. In the case that the small control property does not hold, another formula for constructing continuous state feedback controllers, with small control magnitude near the origin, to achieve robust practical stability is presented.
Wu, Jenq-Lang and Yung, Chee-Fei
"ON STATE-FEEDBACK CONTROLLER SYNTHESIS FOR A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS WITH UNCERTAINTIES,"
Journal of Marine Science and Technology: Vol. 18:
5, Article 5.
Available at: https://jmstt.ntou.edu.tw/journal/vol18/iss5/5