linear time invariant system

A linear time invariant system (LTI) is a linear dynamical system T(p),

y(k) =T(p)u(k),

with parameter p that is time independent. y(k) denotes the system output and u(k) denotes the input. The independent variable k can be denoted as time, index for a discrete sequences or differential operaters (e.g. such as s in Laplace domain or ω in frequency domain).

For example, for a simple mass-spring-dashpot system, the system parameter p can be selected as the mass m, spring constant k and damping coefficient d. The input u to the said system can be chosen as the force applied to the mass and the output y can be chosen as the mass’s displacement.

LTI system has the following properties.


If y1=Tx1 and y2=Tx2, then

Time Invariance:

If y(k)=Tx(k), then


A LTI system can be represented with the following:

Note that all transfer functions are LTI systems, but not all state-space equations are LTI systems.

Title linear time invariant system
Canonical name LinearTimeInvariantSystem
Date of creation 2013-03-22 14:22:25
Last modified on 2013-03-22 14:22:25
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 11
Author Mathprof (13753)
Entry type Definition
Classification msc 93A10
Synonym LTI
Related topic Controllability
Related topic Observability
Related topic SystemDefinitions