Zeitvariiertes

Zeitvariiertes is a term used in German-language technical and scientific literature to describe processes, systems, or models whose defining characteristics change over time. It is the counterpart to zeitinvariant (time-invariant) and is applied whenever parameters, structures, or dynamics are not constant. In this sense, a zeitvariiertes system does not have fixed behavior, but evolves as time progresses due to aging, environmental changes, or deliberate adaptation.

In formal descriptions, zeitvariiertes systems are characterized by time-dependent components. In signal processing, a zeitvariiertes system has an impulse response h(t, τ) that depends on both the observation time t and the input time τ, so the output is y(t) = ∫ h(t, τ) x(τ) dτ. This contrasts with time-invariant systems, where h(t, τ) = h(t − τ) and the output is a simple convolution. State-space representations are also time-varying: ẋ(t) = A(t) x(t) + B(t) u(t), y(t) = C(t) x(t) + D(t) u(t). Time variation complicates analysis, often requiring time-frequency methods or numerical identification.

Common domains for zeitvariiertes modeling include control systems, communications, acoustics, and mechanical engineering. Examples range from adaptive or aging mechanisms in control laws, filters or circuits whose parameters drift with temperature, to nonstationary signals in audio and video processing. In practice, identifying and validating zeitvariiertes models demands specialized techniques to track parameter changes, ensure stability, and assess performance under evolving conditions.

Overall, zeitvariiertes describes a fundamental class of dynamic behavior reflecting temporal evolution, and it is central to accurately modeling real-world systems that do not maintain fixed dynamics.