Uniform Global Asymptotic Stability for Time-Invariant Delay Systems

被引:0
|
作者
Karafyllis, Iasson [3 ]
Pepe, Pierdomenico [4 ]
Chaillet, Antoine [1 ,2 ]
Wang, Yuan [5 ]
机构
[1] L2S CentraleSupelec, Gif Sur Yvette, France
[2] Univ Paris Saclay, Gif Sur Yvette, France
[3] Natl Tech Univ Athens, Math Dept, Athens 15780, Greece
[4] Univ Aquila, Informat Engn Comp Sci & Math Dept, I-67100 Laquila, Italy
[5] Florida Atlantic Univ, Math Sci Dept, Boca Raton, FL 33431 USA
来源
2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC) | 2022年
关键词
OUTPUT STABILITY; LYAPUNOV; INPUT;
D O I
10.1109/CDC51059.2022.9992709
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
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.
引用
收藏
页码:6875 / 6880
页数:6
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