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Deadband is also known as hysteresis and is the amount of a measured variable (pressure, temperature, etc.) between the point where a switch closes and then re-opens. It can be implemented is software if you have an analog input (i.e., open at 1.02 PSI, close at 0.98 PSI) or designed into a switching mechanism. Often the deadband of a switch is fixed and cannot be adjusted. A typical example is in a wall thermostat in your house.
They are often used in low pressure systems to bypass excess air when the majority of zone dampers are closed. TrueZONE Bypass Dampers (CPRD) are round static pressure relief dampers. They are used in forced-air bypass applications to relieve excess static pressure when some of the zone dampers are closed.