Design of finite-time stabilizing controllers for nonlinear dynamical systems

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 Holder continuous Lyapunov functions. In this paper, we extend the finite-time stability theory to revisit time-invariant dynamical systems and to address time-varying 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 vector Lyapunov function approach to study finite-time stabilization of sets for large-scale dynamical systems which is essential in formation control of multiple agents.