This book deals with the analysis, the identification and the control of a special class of systems with hysteresis. This nonlinear behaviour is encountered in a wide variety of processes in which the input–output dynamic relations between variables involve memory effects. Examples are found in biology, optics, electronics, ferroelectricity, magnetism, mechanics and structures, among other areas. In mechanical and struc- tural systems, hysteresis appears as a natural mechanism of materials to supply restoring forces against movements and dissipate energy. In these systems, hysteresis refers to the memory nature of inelastic behaviour where the restoring force depends not only on the instanta- neous deformation but also on the history of the deformation.
The detailed modelling of these systems using the laws of physics is an arduous task, and the obtained models are often too complex to be used in practical applications involving characterization of systems, identification or control. For this reason, alternative models of these complex systems have been proposed.