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I have a system with three inductors connected together at a common point.

The unconnected ends of each inductor is connected to an independent voltage source.

Basically I want to get three expressions for the dynamics of the currents with V1, V2 and V3 as inputs.

i.e. i need to eliminate the intermediary variable VT.

I want to write the state equations for the system in the following format (state space form):

The system and, how far i got is below:

I don't know how to proceed from here.

Or is it impossible to get it into the format I want?

The unconnected ends of each inductor is connected to an independent voltage source.

Basically I want to get three expressions for the dynamics of the currents with V1, V2 and V3 as inputs.

i.e. i need to eliminate the intermediary variable VT.

I want to write the state equations for the system in the following format (state space form):

The system and, how far i got is below:

I don't know how to proceed from here.

Or is it impossible to get it into the format I want?