The frequency-domain technique, which is commonly used for analyzing and designing feedback control systems, is only suitable for linear, time-invariant systems.

The time-domain or state-space approach can handle nonlinear, time-varying, and multiple-input, multiple-output systems.

In the state-space representation, a particular subset of system variables, identified as state variables, is used to construct simultaneous, first-order differential equations for an nth-order system, labeled as state equations.

Consider an RLC circuit. Given that the network is second-order, it's necessary to employ two simultaneous first-order differential equations.

The quantities that are differentiated in the derivative equation for the energy-storage elements - the inductor and the capacitor are the state variables.

Kirchhoff's voltage and current laws are used to express the non-state variables as linear combinations of the state variables and the input.

These results are substituted into the original derivative equations to obtain the state equations.

The output equation is the current through the resistor.

The final step involves representing these equations in a vector-matrix form to acquire the state-space representation of the given electrical network.