Mateamticas

Control System.


A control system converts an input signal x(t) to an
output signal y(t). The transformation is done by the
system is denoted for ������



Where y(t) is the controlledvariable and
acting signal.

x(t) is the

Time - Invariant System.
A system is called time-invariant if the output is always the same

faced the same input, no matter the time instant at whichthe entry
applies.

In a few words, a time-invariant system is one that does not depend
on when it occurs: the output signal doesn't change with the input
delay.

Time – Variant System.
Inthis systems, the outputs responds depending of the right
moment where we apply the input.

In a few words, They are systems that answer of different way still
when the parameters of input are thesame.

X (t-t0)

y(t)

Time - Invariant System.

Time Invarinat System
Solutions Manual to Linear Systems
Theory
Hespanha,J

Time - Invariant System.
A time-invariant system is onewhere a time delay (or

shift) in the input sequence causes a equivalent time
delay in the system's output sequence. Keeping in mind

that n is just an indexing variable we use to keep track of
ourinput and output samples, let's say a system provides

an output y(n) given an input x(n), or:

x(n)

y(n)

ec.1.23

Time - Invariant System.
For a system to be time invariant, with ashifted version of the

original x(n) input applied, x'n, the following applies:

������′ ������ = ������ ������ + ������

→ ������′ ������ = ������ ������ + ������

������. ������������

Wherek is some integer representing k sample period time
delays. For a system to be time invariant expression (1-24) must

hold true for any integer value of k and any input sequence.

Accuracyagainst Simplicity.
To obtain a reasonably simplified mathematical model, it
is often necessary to ignore certain physical properties
inherent to the system. In particular, if it is intended to...