time invariant

A dynamical systemMathworldPlanetmathPlanetmath is time-invariant if its generating formula is dependent on state only, and independent of time. A synonym for time-invariant is autonomousMathworldPlanetmath. The complement of time-invariant is time-varying (or nonautonomous).

For example, the continuous-time system x˙=f(x,t) is time-invariant if and only if f(x,t1)f(x,t2) for all valid states x and times t1 and t2. Thus x˙=sinx is time-invariant, while x˙=sinx1+t is time-varying.

Likewise, the discrete-time system x[n]=f[x,n] is time-invariant (also called shift-invariant) if and only if f[x,n1]f[x,n2] for all valid states x and time indices n1 and n2. Thus x[n]=2x[n-1] is time-invariant, while x[n]=2nx[n-1] is time-varying.

Title time invariant
Canonical name TimeInvariant
Date of creation 2013-03-22 15:02:14
Last modified on 2013-03-22 15:02:14
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 5
Author Mathprof (13753)
Entry type Definition
Classification msc 00A05
Related topic AutonomousSystem
Defines time-invariant
Defines shift-invariant