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Signals and Systems by Smarajit Ghosh

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9.8 SOLUTION OF THE STATE EQUATION

For time invariant system, the state equation is given by

 

image which is divided into two types as follows:
  1. homogeneous state equation
  2. non-homogeneous state equation

The equation is said to be homogeneous if A is a constant matrix and U is a zero vector. In this case no control forces are applied. The equation is said to be non-homogeneous if A is constant matrix and U is a non-zero vector. In the first case discharging a charged capacitor is an example while in the second case total response is an example.

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