What is hysteresis in the context of control systems?

Hysteresis in the context of control systems refers to the dependence of the output on the system's history. It describes the phenomenon where the output of a system is not solely determined by its current input but is also influenced by its past states or inputs. This is particularly important in systems with switching elements, like relays or thermostats, where the output remains in a certain state until a threshold is crossed, regardless of subsequent changes in input. This characteristic can lead to different output values for the same input depending on the previous state of the system, thereby exhibiting a form of memory. Understanding hysteresis is crucial in control system design to prevent issues related to instability, oscillation, or unintended behavior due to the historical influence on system responses.