Title :
A converse Lyapunov theorem for semiglobal practical asymptotic stability and application to cascades-based control
Author :
Chaillet, Antoine ; Loría, Antonio
Author_Institution :
CNRS
Abstract :
We present a converse Lyapunov result for nonlinear time-varying systems that are uniformly semiglobally asymptotically stable. This stability property pertains to the case when the size of initial conditions may be arbitrarily enlarged and the solutions of the system converge, in a stable way, to a closed ball that may be arbitrarily diminished by tuning a design parameter of the system (typically but not exclusively, a control gain). This result is notably useful in cascaded-based control when uniform practical asymptotic stability is established without a Lyapunov function, e.g. via averaging. We provide a concrete example by solving the stabilization problem of a hovercraft
Keywords :
Lyapunov methods; asymptotic stability; cascade control; nonlinear systems; time-varying systems; Lyapunov function; cascades-based control; converse Lyapunov theorem; hovercraft stabilization; initial conditions; nonlinear time-varying system; semiglobal practical asymptotic stability; Asymptotic stability; Concrete; Control systems; Lyapunov method; Nonlinear control systems; Output feedback; Sampling methods; Size control; Time varying systems; USA Councils;
Conference_Titel :
Decision and Control, 2006 45th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
1-4244-0171-2
DOI :
10.1109/CDC.2006.377364