First order systems are the simplest linear systems with dynamics.

• First order systems satisfy a first order differential equation:
• tdx/dt + x(t) = G_dcu(t)
• x(t)  =  Response of the System,
• u(t)  =  Input to the System,
• t  =  The System Time Constant,
• G_dc  =  The DC Gain of the System.

• First order systems have a transfer function with a single pole in the denominator:
• G(s) = G_dc/(st + 1)

• First order systems have an impulse response (response to an impulse with unit area - starting from zero initial conditions):
• x(t) = (G_dc/t)e^-t/t

• First order systems have a step response (response to a unit step - starting from zero initial conditions):
• x(t) = G_dcu(t)(1 - e^-t/t)