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Design of finite-time stabilizing controllers for nonlinear dynamical systems. (English) Zbl 1166.93013
Summary: 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.
MSC:
93D05Lyapunov and other classical stabilities of control systems
93A15Large scale systems
93C10Nonlinear control systems