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.


93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93A15 Large-scale systems
93C10 Nonlinear systems in control theory
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