Chapter

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

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems

Published by Princeton University Press

Published in print December 2011 | ISBN: 9780691153469
Published online October 2017 | e-ISBN: 9781400842667
Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions

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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

Chapter.  10201 words.  Illustrated.

Subjects: Applied Mathematics

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