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The wikipedia article on bang bang control (aka hysteresis control) states that one of the practical issues with bang bang control is an oscillating error signal around the desired setpoint :

First, depending on the width of the hysteresis gap and inertia in the process, there will be an oscillating error signal around the desired set point value (e.g., temperature), often saw-tooth shaped. Room temperature may become uncomfortable just before the next switch 'ON' event.

I cannot find any papers in the control theory literature that describe this issue. I'm looking for one or more published research papers that describe the problem.

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With ``bang-bang.'' When it gets too cold bang, switch on the heater. As soon as the temperature rises above 60° bang, switch off the heater. Too hot? Bang, the air conditioner starts, and so on. Thats why the room temperature becomes uncomfortable before switching. And the error will oscillate, (saw tooth as the temperature variation will be slow..somewhat exponentially up and exponentially down) between each on and off cycle.

Some references that discuss this :

1) "Modified Bang-Bang Control Law for Structural Control Implementation - here.

2) "The bang-bang funnel controller: time delays and case study", 2013 European Control Conference (ECC) July 17-19, 2013, Zürich, Switzerland.here

3) Dancy, Abram P., and Leif E. LaWhite. "Interleaved power converters incorporating bang-bang control." U.S. Patent No. 6,577,109. 10 Jun. 2003.

Hope this helps