C2 Li R R3 C. HE + Vit) R2 L2 v.(t) L3 Figure 1: Circuit Consider the circuit is shown in Figure 1 where vi(t) is the input voltage, vo(t), is the output voltage, L1, L2 and L3 are inductances, C1, C2 and C3 are capac- itances and Ri, R2 and R3 are resistances. (a) Determine a state space model of the circuit. (b) Determine an input/output transfer function of the system. If the system input/output model order is not the same as the order of the state space model, explain why. (c) Using a modal decomposition, determine the controllability and observabil- ity of the system. C2 Li R R3 C. HE + Vit) R2 L2 v.(t) L3 Figure 1: Circuit Consider the circuit is shown in Figure 1 where vi(t) is the input voltage, vo(t), is the output voltage, L1, L2 and L3 are inductances, C1, C2 and C3 are capac- itances and Ri, R2 and R3 are resistances. (a) Determine a state space model of the circuit. (b) Determine an input/output transfer function of the system. If the system input/output model order is not the same as the order of the state space model, explain why. (c) Using a modal decomposition, determine the controllability and observabil- ity of the system