Uniform weak attractivity and criteria for practical global asymptotic stability

Titelangaben

Mironchenko, Andrii:
Uniform weak attractivity and criteria for practical global asymptotic stability.
In: Systems & Control Letters. Bd. 105 (2017) . - S. 92-99.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2017.05.005

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Abstract

A subset of the state space is called uniformly globally weakly attractive if for any neighborhood of and any bounded subset there is a uniform finite time so that any trajectory starting in intersects within the time not larger than . We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attractive set. This result is valid for a wide class of distributed parameter systems, including time-delay systems, switched systems, many classes of PDEs and evolution differential equations in Banach spaces. We apply our results to show that existence of a non-coercive Lyapunov function ensures pUGAS for this class of systems. For ordinary differential equations with uniformly bounded disturbances, the concept of uniform weak attractivity is equivalent to the well-known notion of weak attractivity. It is however essentially stronger than weak attractivity for infinite-dimensional systems, even for linear ones.