Quasiglobal

Quasiglobal is an adjective used in technical disciplines to describe properties that are nearly global in scope. It communicates that a result, method, or property applies across a broad portion of a system’s domain, but not necessarily to every possible state, input, or condition. The exact meaning of quasiglobal is context-dependent and may vary between fields.

In mathematics and dynamical systems, quasiglobal typically denotes results that hold for all initial conditions in a large subset of the state space, often excluding a small exceptional set such as a set of measure zero or a boundary. This contrasts with global statements that hold universally and with local statements that apply only near a particular point.

Common usages include quasiglobal stabilization in control theory, where a feedback law guarantees stability for all initial states except perhaps those lying in a restricted region or on a lower-dimensional subset. In partial differential equations or optimization, quasiglobal results may assert existence, regularity, or convergence over wide domains while acknowledging potential limitations for specific initial data or configurations.

Because quasiglobal is not a formally standardized term, its precise meaning should be defined within each work. When used, authors typically specify the scope of the quasiglobal property, the nature of the exceptional set, and how the concept relates to closely related notions such as global, almost global, or local results.