# Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions

# Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions

This chapter develops a general framework for finite-time stability analysis based on control vector Lyapunov functions. Specifically, it develops a vector comparison system whose solution is finite-time stable and relates this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. The results are specialized to the case of a scalar Lyapunov function to obtain universal finite-time stabilizers for nonlinear systems that are affine in the control. Finally, the utility of the proposed framework is demonstrated using two numerical examples: the first involves a large-scale dynamical system with control signals for each decentralized control channel as a function of time; the second example considers control of thermoacoustic instabilities in combustion processes.

*Keywords:*
finite-time stability, control vector Lyapunov function, vector comparison system, nonlinear dynamical system, scalar Lyapunov function, large-scale dynamical system, control signal, decentralized control, thermoacoustic instabilities, combustion processes

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.