Asymptotic stability for systems with multiple hysteresis nonlinearities

Absolute stability criteria for systems with multiple hysteresis nonlinearities are given in this paper. If the linear subsystem satisfies a simple two part test involving a linear matrix inequality and a simple residue condition, then the nonlinear system is proven to be asymptotically stable. The main stability theorem uses a combination of passivity, Lyapunov, and Popov stability theories to show that the state describing the linear system dynamics must converge to an equilibrium position of the nonlinear closed loop system. The stationary sets that contain all possible equilibrium points are detailed for common types of hystereses, and simple examples are used to illustrate the benefits of the new results.