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Signals and Systems by Smarajit Ghosh

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9.7 TRANSFER FUNCTION DERIVATION FROM THE STATE MODEL

From the state model equations, we can derive the transfer function of the system. From definition of transfer function, we can write

 

image

 

For a linear time-invariant system the dynamics can be written in vector differential form as follows:

 

image

 

y = Cx + Du       (9.50)

 

Taking Laplace transform of Eq. (9.49), we can write

 

sX(s)–x(0) = AX(s)+ BU(s)

 

∴        [sIA] X(s) = BU(s) [Taking x(0) = 0]

 

∴           X (s) = [sIA]−1BU(s)       (9.51)

 

Taking Laplace transform of Eq. (9.50) ...

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