On the stability of discrete-time systems with hysteretic controllers

The problem of deriving a frequency-domain sufficient condition for the global asymptotic stability of a discrete-time system having hysteretic controllers is considered. It is suggested that the hysteretic characteristic be replaced by a function of the form f(y, ẏ) where y(t) is the input to the controller. This allows the problem to be reformulated to that of deriving a sufficient condition for the stability of a two-controller system where both the controllers are nonhysteretic. This latter problem is solved by embedding it into a two-variable problem. Numerical examples are presented which illustrate the results.