A. Bacciotti and L. Rosier, “Liapunov Functions and Stability in Control Theory,” Springer-Verlag, London, 2001.

has been cited by the following article:

• TITLE: Continuous Stabilizing of First Order Single Input Nonlinear Systems

  AUTHORS: Aref Shahmansoorian

  KEYWORDS: Control Lyapunov Function, Inverse Optimality, Sontag’s Formula

  JOURNAL NAME: Intelligent Control and Automation, Vol.2 No.3, August 8, 2011

  ABSTRACT: In this paper, stabilizability of first order nonlinear systems by a smooth control law is investigated. The main results are presented by the examples and finally summarized in a lemma. The proof for the lemma is according to Sontag’s formula. In addition, it is explained that using weak control Lyapunov functions in Sontag’s formula generates (possibly nonsmooth) the control law, which globally stabilizes the system-globally asymptotic stability needs more investigation.