Averaging of nonsmooth systems using dither

Authors:
Luigi Iannelli;Karl Henrik Johansson;Ulf T. JöNsson;Francesco Vasca
Affiliations:
Department of Engineering, University of Sannio, Piazza Roma, 21, 82100 Benevento, Italy;Department of Signals, Sensors and Systems, Royal Institute of Technology, Osquldas vägen, 10 100 44 Stockholm, Sweden;Division of Optimization and Systems Theory, Royal Institute of Technology, Lindstedts vägen, 25 100 44 Stockholm, Sweden;Department of Engineering, University of Sannio, Piazza Roma, 21, 82100 Benevento, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

It was shown by Zames and Shneydor and later by Mossaheb that a high-frequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems can be narrowed using dither, as long as the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. The averaged system is proven to approximate the dithered system with an error of the order of dither period.