Design of finite‐time stabilizing controllers for nonlinear dynamical systems

Abstract 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 extend the finite‐time stability theory to revisit time‐invariant dynamical systems and to address time‐varying dynamical systems. Specifically, we develop a Lyapunov‐based stability and control design framework for finite‐time stability as well as finite‐time tracking for time‐varying nonlinear dynamical systems. Furthermore, we use the vector Lyapunov function approach to study finite‐time stabilization of compact sets for large‐scale dynamical systems. Copyright © 2008 John Wiley & Sons, Ltd.