systemnorm

Systemnorm is a term used in multiple disciplines to denote a standard method for quantifying how a system responds to external inputs. In engineering and applied mathematics, it is commonly associated with norms that measure gain or energy amplification from input to output.

In control theory, the most widely used instantiation is the H-infinity norm. For a stable linear time-invariant system with transfer function G(s), the H∞ norm is defined as the supremum of the largest singular value of G(jω) over all frequencies ω. This supremum represents the worst-case gain from input to output for square-integrable signals and provides a bound that is central to robust control design and stability analysis. Other norms, such as the L2-induced norm, are also used to quantify energy amplification and may coincide with the H2 norm in certain contexts. Systemnorm values guide controller synthesis, performance benchmarking, and the assessment of robustness to disturbances and model uncertainty.

In other disciplines, the phrase may refer more broadly to normative standards within a system or organization, describing expected behaviors, interfaces, and procedures that define how the system operates. As a polysemous term, the precise meaning of systemnorm depends on the field and the context.