EE 3120 Linear Systems Analysis
Chapter 2 Lecture 2 Time Invariance
A system that has characteristics and properties that do not change with time is timeinvariant.
For a timeinvariant, memoryless system the output is the same no matter the time the input is
applied.
A timevarying system
( )
1
u t
=
( )
sin( ) ( )
y t
t u t
=
for at
t
A timeinvariant system
=
( )
sin
( )
y t
u t
( )
1
u t
=
for at
t
(0)
sin(1)
y
=
(1)
sin(1)
y
=
(0)
sin(0)(1)
0
y
=
=
(1)
sin(1)(1)
0.84
y
=
=
(2)
sin(1)
y
=
(2)
sin(2)(1)
.909
y
=
=
For any memoryless system is linear iff it can be written
It is also timeinvariant
iff
is constant.
( )
( ) ( )
y t
a t u t
=
( )
a t
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EE 3120 Linear Systems Analysis
Chapter 2 Lecture 2 Time Invariance
For a linear, time invariant (LTI) system system with memory, the initial state and input are the
same, no matter what time they are applied, the output will always be the same.
In other words – if the state and input are shifted by T, then the output is shifted by T.
Properties of TI system are independent of time.
An RLC circuit is TI if RLC are constant.
The
initial time
is not critical for analysis of a TI system.
We can set initial time
= 0 and start to
observe the system or apply input.
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 Fall '08
 ARAVENA
 LTI system theory, Linear Systems Analysis, Linear Time Invariant Lumped Systems

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