Finite-time stabilization of nonlinear dynamical systems via control vector Lyapunov functions

• Published in: Journal of the Franklin Institute 2008-10, Vol.345 (7), p.819-837
• Main Authors: Nersesov, Sergey G., Haddad, Wassim M., Hui, Qing
• Format: Article
• Language: English
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; Finite-time convergence; Finite-time stability; Homogeneity; Non-Lipschitzian dynamics; Vector comparison principle; Vector Lyapunov functions
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2008.04.015

Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using Hölder continuous Lyapunov functions. In this paper, we develop a general framework for finite-time stability analysis based on vector Lyapunov functions. Specifically, we construct a vector comparison system whose solution is finite-time stable and relate this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. Furthermore, we design a universal decentralized finite-time stabilizer for large-scale dynamical systems that is robust against full modeling uncertainty. Finally, we present two numerical examples for finite-time stabilization involving a large-scale dynamical system and a combustion control system.