December 2005
Intermediate to advanced
475 pages
12h 6m
English
Content preview from Signals and Systems
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9.9 CONTROLLABILITY
Any linear time invariant system can be represented by the dynamic equation
and y(t) = Cx(t) + Du(t)
The state x(t) will be controllable at t = t0 when there exists a piecewise continuous input u(t) which will drive the state to any final state x(t) for finite time interval (t − t0) ≥ 0. The system is called controllable if every state of the system is controllable in finite time interval.
For controllability of the system the matrix
[s] = [B AB A2B … An−1B] must have rank n.
If there is no connection between a certain state and input, the state is not controllable as shown in Fig. 9.12.
Fig. ...
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