On the Lyapunov Stability of Bouc-Wen hysteresis model for a class of input signals

This paper discusses the Lyapunov stability of the Bouc-Wen model for a special class of inputs x(t) satisfying the condition x(t)x(t) <; 0 for t > 0. This kind of input signals can be found in many applications. Some examples of this class of inputs are special cases of exponential signals and periodic triangular waves. The current work presents a Lyapunov function which proves the stability of the Bouc-Wen model of classes I, III and V when it is exposed to the aforementioned type of inputs. An application of the presented work here is studied for the active control of hysteretic structures. The results obtained here can be used in the analysis and control of mechanical systems which their hysteretic phenomenon is expressed by the Bouc-Wen model.