Analytic application of Tsypkin´s method relay with hysteresis and dead zone

A method is developed whereby the periodic component of the output of a self-oscillating relay system is obtained without utilising the Fourier series expansion. This way the infinite sums encountered in the application of Tsypkin´s method are avoided and in their place analytic expressions for the real and imaginary parts of Tsypkin functions are arrived at. These results are applied to systems containing relay elements having hysteresis and dead zone.