State-space Modeling – Worked Example

Find a state-space representation for this RLC circuit if the output is the resistor current.

The state-space approach is a unified method for modelling, analysing, and designing a wide range of systems. It is a topic usually discussed in a control systems course. The idea is to select a number of key variables, called 𝘀𝘁𝗮𝘁𝗲 𝘃𝗮𝗿𝗶𝗮𝗯𝗹𝗲𝘀, that capture the dynamic nature of the system.

It consists of two components:

(1) ẋ = Ax + Bu (state equations)

(2) y = Cx + Du (output equation)

In other words, a viable state-space representation requires that both the derivatives of the state variables as well as the system’s output be expressed as a linear combination of the state variables and the input to the system.

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