# Lecture 10: Laplace Transform of State Equations

Schedule
::
Perspective
::
Transfer Functions
:: Laplace Transform ::
Poles and Eigenvalues
::
Time Domain
::
Linear Transformations
::
Special Transformation
::
Controllability
::
Discrete-Time

then

We find then that

From the state equation we obtain

and from the output equation,

Let us solve for from the first:

(Why the identity?) Watch the order!

Inverse transform:

Identify zero-input components and zero-state components.
Transfer function:

When we talk about the Laplace transform of a vector, we will mean to
apply the transform element by element. Thus, if

then

We find then that

From the state equation we obtain

and from the output equation,

Let us solve for from the first:

(Why the identity?) Watch the order!

Let . We have

Inverse transform:

Identify zero-input components and zero-state components.

Output:

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by the Contributing Authors.
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admin. (2006, June 08). Lecture 10: Laplace Transform of State Equations. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/10_3node3.html.
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