Page 394 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 71 STATE SPACE ANALYSIS

In matrix form

7.5. Consider the RLC circuit shown in Fig. 7-5. Let the output y(t) be the loop current.
Find a state space representation of the circuit.
We choose the state variables q,(t) = i,(t) and q2(l) = u,(t). Then by Kirchhoffs law we
get
L4,(t) + Rs,(t) + q2(1) =x(t)
cq,(t) =dl)
Y(t) =41(t)
Rearranging and writing in matrix form, we get

Fig. 7-5 RLC circuit.

7.6. Find a state space representation of the circuit shown in Fig. 7-6, assuming that the
outputs are the currents flowing in R, and R,.
We choose the state variables q,(t) = i,(t) and q2(t) = r;(t). There are two voltage sources
and let x,(t) = u,(t) and xJt) = u2(t). Let y,(t) = i,(t) and y,(t) = i,(t). Applying krchhoffs
law to each loop, we obtain