Robust stability and performance analysis of systems with hysteresis nonlinearities

There has been extensive work done in recent years on the analysis and synthesis of systems having memoryless, sector bounded nonlinearities and uncertainties. In this paper we take a fundamentally different approach to develop tests of the stability of systems with hysteresis nonlinearities which, in general, have memory and are not sector bounded. Using an operator perspective, and considering a hysteresis that obeys a strict circulation direction, we develop a transformation which converts a hysteresis nonlinearity into a passive operator. Our main stability theorem then provides a simple Nyquist test (for a SISO system) or a linear matrix inequality (LMI) which is extended to include a provision for a robust performance test. A simple numerical example illustrates the benefit of the multiplier introduced for this class of nonlinearities