Forward completeness does not imply bounded reachability sets and global asymptotic stability is not necessarily uniform for time-delay systems
An example of a time-invariant time-delay system that is uniformly globally attractive and exponentially stable, hence forward complete, but whose reachability sets from bounded initial conditions are not bounded over compact time intervals is provided. This gives a negative answer to two current conjectures by showing that (i) forward completeness is not equivalent to robust forward completeness (i.e. boundedness of reachability sets) and (ii) global asymptotic stability is not equivalent to uniform global asymptotic stability. In addition, a novel characterization of robust forward completeness for systems having a finite number of discrete delays is provided. This characterization relates robust forward completeness of the time-delay system with the forward completeness of an associated nondelayed finite-dimensional system.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Verification of Nonblockingness in Bounded Petri Nets With Minimax Basis Reachability Graphs
This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the rea…
BlockingReachability of Dimension-Bounded Linear Systems
In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A …
Non-Blockingness Verification of Bounded Petri Nets Using Basis Reachability Graphs -- An Extended Version With Benchmarks
In this paper, we study the problem of non-blockingness verification by tapping into the basis reachability graph (BRG). Non-blockingness is a property that ensures that all pre-specified tasks can be completed, which is…
Quadratic Characterizations for Reachability Analysis of Neural Networks
Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for construct…
No-Regret Learning in Games is Turing Complete
Games are natural models for multi-agent machine learning settings, such as generative adversarial networks (GANs). The desirable outcomes from algorithmic interactions in these games are encoded as game theoretic equili…