A time-variant system is a

system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ...

whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also changes other parameters and behavior. Time variant systems respond differently to the same input at different times. The opposite is true for

time invariant In control theory, a time-invariant (TIV) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is ...

systems (TIV).

Overview

There are many well developed

techniques Technique or techniques may refer to: Music * The Techniques, a Jamaican rocksteady vocal group of the 1960s *Technique (band), a British female synth pop band in the 1990s * ''Technique'' (album), by New Order, 1989 * ''Techniques'' (album), by M ...

for dealing with the response of linear time invariant systems, such as

Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...

and

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

s. However, these techniques are not strictly valid for time-varying systems. A system undergoing slow time variation in comparison to its time constants can usually be considered to be time invariant: they are close to time invariant on a small scale. An example of this is the aging and wear of electronic components, which happens on a scale of years, and thus does not result in any behaviour qualitatively different from that observed in a time invariant system: day-to-day, they are effectively time invariant, though year to year, the parameters may change. Other linear time variant systems may behave more like nonlinear systems, if the system changes quickly – significantly differing between measurements. The following things can be said about a time-variant system: * It has explicit dependence on time. * It does not have an

impulse response In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an Dirac delta function, impulse (). More generally, an impulse ...

in the normal sense. The system can be characterized by an impulse response except the impulse response must be known at each and every time instant. * It is not stationary

Linear time-variant systems

Linear-time variant (LTV) systems are the ones whose parameters vary with time according to previously specified laws. Mathematically, there is a well defined dependence of the system over time and over the input parameters that change over time. :

y(t) = f ( x(t), t)

In order to solve time-variant systems, the algebraic methods consider initial conditions of the system i.e. whether the system is zero-input or non-zero input system.

Examples of time-variant systems

The following time varying systems cannot be modelled by assuming that they are time invariant: * The Earth's thermodynamic response to incoming

Solar irradiance Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre (W/ ...

varies with time due to changes in the Earth's albedo and the presence of

greenhouse gas A greenhouse gas (GHG or GhG) is a gas that Absorption (electromagnetic radiation), absorbs and Emission (electromagnetic radiation), emits radiant energy within the thermal infrared range, causing the greenhouse effect. The primary greenhouse ...

es in the atmosphere. * Discrete wavelet transform, often used in modern signal processing, is time variant because it makes use of the

decimation Decimation, Decimate, or variants may refer to: * Decimation (punishment), punitive discipline * Decimation (signal processing), reduction of digital signal's sampling rate * Decimation (comics), 2006 Marvel crossover spinoff ''House of M'' * ''D ...

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References

Control theory

Overview

Linear time-variant systems

Examples of time-variant systems

See also

References