EE2010
Systems and Control
(Chapter 2)
2-1
Static and Dynamic System
System is static (also called memoryless) if output is a function of the
input at the present time only, i.e.,
y
(
t
) =
K
×
u
(
t
)
Example is a resistor,
V
(
t
) =
i
(
t
) ×
R.
Output of a dynamic system (also called non-zero memory) at time
t
depends on past or future values of the input
u
in addition to the
present time, i.e.,
y
(
t
) =
f
{…,
u
(
t
+
1),
u
(
t
),
u
(
t
1),
…}
Examples include,
Capacitors,
Inductors,
Basic System Properties
t
d
i
C
t
V
0
)
(
1
)
(
dt
t
di
L
t
V
)
(
)
(

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EE2010
Systems and Control
(Chapter 2)
2-2
An important characteristic of dynamic systems
is that output signal must be continuous
Consider battery charging in a mobile phone
(a simple RC circuit):
For
V
c
(
t
) to change in a step manner
when switch is closed,
i
(
t
) needs to be infinite.
However, current in circuit must be finite
because voltage source is finite. Therefore
V
c
(
t
) must be continuous since
Likewise, current flowing in an inductor must
be continuous because
dt
t
dV
C
t
i
c
)
(
)
(
dt
t
dV
c
)
(
dt
t
dV
c
)
(
dt
t
di
L
t
V
L
L
)
(
)
(

EE2010
Systems and Control
(Chapter 2)
2-3
Causal and Non-Causal System
System is causal or non-anticipatory if the output signal,
y
(
t
0
), at
t
=
t
0
,
depends only on values of the input,
u
(
t
), for
t
≤
t
0
Causality implies that the system does not respond to an input event
until that event actually occurs, i.e., the response to an event beginning
at
t
=
t
0
is non-zero only for
t
≥
t
0
All static/memoryless systems are causal since the output depends
only on the current value of the input. All naturally occurring systems
are causal or appear to be causal

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EE2010
Systems and Control
(Chapter 2)
2-4
Engineering applications, whose independent variable is not time,
may be non-causal, e.g., an image processing software
Linear and Non-linear Systems
Linear systems satisfy the properties of
Additivity:
y
(
t
) =
f
{
x
1
(
t
) +
x
2
(
t
)} =
f
{
x
1
(
t
)} +
f
{
x
2
(
t
)}
Scaling:
If
y
(
t
) =
f
{
x
(
t
)}, then
y
(
t
) =
f
{
x
(
t
)}