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Signals and Systems by Smarajit Ghosh

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9.4 NON-UNIQUENESS OF THE STATE MODEL

The state model of any system is not unique. Alternate representations are possible for any given system. Let us consider a state model of a system as given below.

 

image

 

y = Cx + Du       (9.11)

 

Let the transformation be

 

x = Mz       (9.12)

 

where M is a non-singular constant matrix.

∴ Using Eq. (9.12), Eq. (9.10) can be written as

 

image

 

image

 

Using Eq. (9.12), Eq. (9.11) can be written as:

 

y = CMz +

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