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.