Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
The response of a state-space model Eq.(1.8) to initial
conditions, i.e., its initial state
, is given by
and the complete response of a linear system is given by the
sum of its forced response (such as the impulse response) and
its initial-condition response.
In our force-driven mass example, with the external force set to zero,
we have, from Eq.(1.9) or Eq.(1.11),
Thus, any initial velocity
remains unchanged, as physically expected.
The initial position
remains unchanged if the initial velocity is
zero. A nonzero initial velocity results in a linearly growing
position, as physically expected. This response to initial conditions
can be added to any forced response by superposition. The forced
response may be computed as the convolution of the input driving force
with the impulse response Eq.(1.11).
Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]