Finite-time stability for time-varying nonlinear dynamical systems
- 1 June 2008
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 4135-4139
- https://doi.org/10.1109/acc.2008.4587141
Abstract
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies non-uniqueness of system solutions in backward time, such systems possess non-Lipschitzian dynamics. In this paper, we address finite-time and uniform finite-time stability of time-varying systems. Specifically, we provide Lyapunov and converse Lyapunov conditions for finite-time stability of a time-varying system. Furthermore, we show that finite-time stability leads to uniqueness of solutions in forward time. In addition, we establish necessary and sufficient conditions for continuity of the settling-time function of a nonlinear time-varying system.Keywords
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