Dither in linear systems with memoryless nonlinearity and optimal control

The injection of a high-frequency signal, commonly called dither, into a nonlinear system may improve its performance. Stability of the dithered system is related to that of its corresponding model - the smoothed system, of which the nonlinear element N_s (smoothed nonlinearity) is the convolution of the dither distribution and the original nonlinearity N. The dither amplitude, but not its frequency affects the sector of N_s. The importance of dither frequency is found in its effect on the deviation of the smoothed system from the dithered system, and the deviation can be improved as dither frequency increases. The dither with a sufficiently high frequency may result in the smoothed system´s output and the dithered system´s output as close as desired. An optimal controller and a dither, as an auxiliary of the controller, are simultaneously introduced to make the stability more robust, no matter whether the controlled plant is stable or not. The main characteristic of this paper is that an algorithm is proposed to find a lower bound on dither amplitude to stabilize the nonlinear feedback system