Force-Driven-Mass Diagonalization Example

To diagonalize our force-driven mass example, we may begin with its state-space model Eq.(1.9):

which is in the general state-space form as needed (Eq.(1.8)). We can see that is already a Jordan block of order 2 [449, p. 368]. (We can change the to 1 by scaling the physical units of .) Thus, the system is already as diagonal as it's going to get. We have a repeated pole at , and they are effectively in series (instead of parallel), thus giving a ``defective'' matrix [449, p. 136].

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.