# Dictionary:State variable

One of the sets of variables which completely describe a system at any time. A state variable may represent a derivative of a quantity which is itself a state variable, allowing differential equations to be expressed as a set of linear simultaneous equations. For example, the voltage drop around an electrical circuit which includes capacitance, inductance, and resistance may be expressed by the differential equation:

Using state variables of , , and permits this to be written as a set of three simultaneous equations:

, and

See also *parameter*.