时滞系统的全局渐近稳定性必然一致吗？
Is Global Asymptotic Stability Necessarily Uniform for Time-Delay Systems?
摘要：
对于时不变有限维系统，全局渐近稳定性（GAS）等价于一致全局渐近稳定性（UGAS），后者要求解的衰减率和瞬态超调在有界的初态集上是一致的.本文研究这种关系的时不变时滞系统。我们表明，UGAS和GAS是等价的，这类系统的鲁棒前向完备性的假设下，即假设下，从任何有界集的初态在任何有限的时间范围是有界的。我们还表明，如果状态空间是一个空间中的一个特定的家庭的Sobolev或持有人的空间，然后气体是等价的UGAS和强大的前向完备性举行。基于这些等价关系，我们提供了一个新的Lyapunov特性的气体（和UGAS）在上述空间。
英文摘要：
For time-invariant finite-dimensional systems, it is known that global asymptotic stability (GAS) is equivalent to uniform global asymptotic stability (UGAS), in which the decay rate and transient overshoot of solutions are requested to be uniform on bounded sets of initial states. This paper investigates this relationship for time-invariant delay systems. We show that UGAS and GAS are equivalent for this class of systems under the assumption of robust forward completeness, i.e. under the assumption that the reachable set from any bounded set of initial states on any finite time horizon is bounded. We also show that, if the state space is a space in a particular family of Sobolev or Holder spaces, then GAS is equivalent to UGAS and that robust forward completeness holds. Based on these equivalences, we provide a novel Lyapunov characterization of GAS (and UGAS) in the aforementioned spaces.
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