Input-output stability of feedback systems with hysteresis for inputs satisfying bounding conditions

This paper considers the input-output stability of feedback systems made up of a time-invariant linear element and a hysteresis element. From previous work, it is appreciated that for any input such that the two norm of the product of its slope and an increasing exponential function is finite, if the linear subsystem satisfies a Popov inequality for a sector bound and if the slope of the hysteresis lies within the same sector bound, then the outputs of the system are ensured to be finite for all time. Based on this, the paper develops a practical method for determining stabilizing controllers by numerical methods. To illustrate the usefulness and the potential of the method, two numerical examples are provided in which the plants are described by non-rational transfer functions.