Page 760 - Mechanical Engineers' Handbook (Volume 2)

6 Controllability and Observability 751

Figure 4 Decomposition of linear system based on controllability and observability.

controllability or observability is a less common occurrence. Conclusions concerning con-
trollability and observability are obvious in many of these cases but less so in others.
Consider the electrical circuit in Fig. 5. The state-space equation for the system is given
by

R R 3 R 1 3 2
(69)
1
1
x
˙ x
L
L
1

1
1
L 1 u(t)
˙ x
3
2 R 3 R R x 2 0
L 2 L 2

Figure 5 State variables for RL circuit.