A dynamical system is time-invariant if its generating formula is dependent on state only, and independent of time. A synonym for time-invariant is autonomous. The complement of time-invariant is time-varying (or nonautonomous).
For example, the continuous-time system is time-invariant if and only if for all valid states and times and . Thus is time-invariant, while is time-varying.
Likewise, the discrete-time system is time-invariant (also called shift-invariant) if and only if for all valid states and time indices and . Thus is time-invariant, while is time-varying.
|Date of creation||2013-03-22 15:02:14|
|Last modified on||2013-03-22 15:02:14|
|Last modified by||Mathprof (13753)|