9.8 SOLUTION OF THE STATE EQUATION
For time invariant system, the state equation is given by
which is divided into two types as follows:
- homogeneous state equation
- 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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