State Space Equation

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Solution: The state variables we will use are as follows:

The state-space equations we will have using nodal analysis and mesh analysis are:

The output equation y(t) is equal to:

We will have the following state-space equations in matrix form:

The output equation in matrix form is:

To get the transfer function, we need to get the Laplace transform of each state-space equations and the output equation. We will have:

Since the output requires the inductor current, we will equate the state-space equations in terms of inductor current:

Substitute it to the equation of the output, we have the transfer function of:

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