This work develops a probability broadcast feedback controller for an ensemble of stochastically behaving cellular units exhibiting hysteresis. Previous work has developed asymptotically stable control laws for ideal on-off cellular units without any hysteresis or time lag. This work extends previous results by developing an asymptotically stable control law for an ensemble of cells that experience an arbitrary refractory period after a change in output, during which time the cell output is fixed. This refractory period describes the behavior of hysteretic cells such as shape memory alloy (SMA) actuators or biological cell migration. Conditions for stability are obtained using a stochastic Lyapunov function. Simulation of SMA actuators demonstrates the application of the new control law to practical hysteresis loops.
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