Stability of Uncertain Systems with Hysteresis Nonlinearities

Stability of systems with hysteresis nonlinearities, parametric uncertainty and finite dimensional unmodelled dynamics is considered. Conditions for exponential decay of the signals in the system to an equilibrium position are given. The equilibrium is generally not unique. The stability condition is given in terms of a frequency domain inequality, which involves the transfer function of the nominal system and a multiplier, The search for a suitable multiplier can be performed by use of convex optimization in terms of linear matrix inequalities. A simple example is given that illustrates our result