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This is already the norm in sensitive electronic systems which require battery back-up.
A simple circuit would have incoming AC power supplying a battery charger and a power supply. The power supply puts out "x" volts DC to the equipment. The battery charger supplies "x-1" volts DC to the batteries.
Place a diode in-line between the batteries and the power supply.
The slightly higher power supply voltage reverse biases the diode, preventing current flow from the battery.
When the power supply fails, the batteries will instantly (practically speaking) power the load.
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