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.
Highlights
Consider the following nonlinear system:x f x g x u (1)Definition [1]: A differentiable positive definite and radially unbounded function V x : Rn R 0 is called a CLF for the system (1), if for each x 0, (2)If there exist nonzero points where V x 0, V x is sometimes referred to as Weak ControlLyapunov Function (WCLF) [2,3].satisfies the small control property [3]
Satisfies the small control property [3]. It is well known there is a class of nonlinear systems that can not be stabilized by a continuous time-invariant feedback
Stabilizability of nonlinear systems is studied in literatures [7,8]
Summary
If there exist nonzero points where V x 0 , V x is sometimes referred to as Weak Control. Lyapunov Function (WCLF) [2,3]. Stabilizability of nonlinear systems is studied in literatures [7,8]. In [3] Brockett defines a necessary condition for stabilizability of nonlinear systems by a continuous feedback. In this paper sufficient condition for stabilizability of single input nonlinear systems by a continuous feedback is introduced
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
