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Lecture 10: Time Domain Solution

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

We begin by defining a new function. For a square matrix (as in the state transition matrix) we define

(Taylor series). This is directly analogous to for scalars, except that all arithmetic is done using matrices. This is computed using the exmp function in M ATLAB , not exp . Note (show this)

The solution to the DE

is given by

Show that it works by substitution.

Computing the matrix exponential: One way:

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 08). Lecture 10: Time Domain Solution. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/node5_1.html. This work is licensed under a Creative Commons License