Linear controller analysis and design for systems with input hystereses nonlinearities

An output feedback control analysis and design framework for linear systems with input hystereses nonlinearities is developed. Specifically, by transforming the hystereses nonlinearities into dissipative input–output dynamical operators, dissipativity theory is used to analyze and design linear controllers for systems with hysteretic actuators. The overall framework guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system state associated with the plant and the controller. Furthermore, the remainder of the state associated with the hysteresis dynamics is shown to be semistable; that is, solutions of the hysteretic system converge to Lyapunov stable equilibrium points determined by the system initial conditions.