This paper considers the stability of feedback systems with discontinuous nonlinearities (relay and backlash).
It is assumed that the feedback system consists of a linear dynamical system characterized by the impulse response and a discontinuous nonlinearity.
First, some stability criteria for a feedback system with relay element are derived by the use of Multiplier method. In the case when the ideal relay is concerned, the relation between the stability criteria given here and the well-known local stability criterion as well as the global stability criterion which was derived by the Liapunov's direct method are discussed.
A new frequency-domain stability criterion for the system containing a relay with dead-zone and hysteresis is given by taking into account the particular characteristics of the nonlinearity.
As the application of stability criterion for the feedback system containing such a relay hysteresis nonlinearity, the stability analysis of a class of PFM system is discussed.
Finally, extended stability criteria for a feedback system with backlash are given by the use of so-called multiplier method and a sufficient condition for the stability is given in the Nyquist plane.

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