Deadband is an area of a signal range or band where no action occurs (the system is dead). Deadband is used in voltage regulators, thermostats, and alarms. The purpose is common, to prevent oscillation or repeated activation-deactivation cycles (called 'hunting' in proportional control systems).

Examples:

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Voltage regulators

In some substations there are regulators that keep the voltage within certain predetermined limits, but there is a range of voltage in-between during which no changes are made, such as, maybe, between 112 to 118 volts (deadband is 6 volts here), or 215 to 225 volts (deadband is 10 volts here).

Thermostats

The furnace in the basement of a house is adjusted automatically by the thermostat to be switched on as soon as the temperature at the thermostat falls to, maybe, 18 °C, and the furnace is switched off by the thermostat as soon as the temperature at the thermostat reaches 22 °C. Then the deadband is 4 °C.

Alarms

A smoke detector at the ceiling of the kitchen starts the alarm as soon as the level of the gases reaching it from the burning toast is at, say, x, then the smoke detector stays in the alarm position until the level of gases have been reduced to level y, after which the smoke detector is reset automatically to "normal". The deadband here is x minus y.

Control theory