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Notes on the Computation of the Incremental Gain of Linear Systems with Saturation.

Romanchuk B. G.

Proceedings of the 34th IEEE CDC, 1995

Abstract

In this paper, the incremental gain properties of a class of single input linear systems with saturation are examined. The main justification of the study of the incremental gain is that it allows some stronger conclusions than can be drawn from the use of the induced norm in the analysis of nonlinear systems. Unfortunately, it appears that having a finite incremental gain is too strong a condition for analysis, a fact which has been noted in the recent paper by Chitour, Liu and Sontag. That paper examines not only finite incremental gain but also more general continuity and differentiability properties of a specific class of systems (the plant must have a neutrally stable dynamics matrix) in continuous time. This present work amplifies those conclusions, as it is shown that the incremental gain does not exist for open loop unstable discrete time plants (even over some bounded signal spaces for which the induced norm exists), and an algebraic technique for bounding the l_2 and L_2 incremental gain for some subset of the open loop stable plants is given. The inequalities which result are the same as those which would result from attempting to force a global quadratic solution to the test for the induced norm given in the recent paper by the author, which indicates that such algebraic tests are telling us about incremental gain magnitudes. The class of plants for which the results are applicable has been generalised at the cost of restricting our attention to the standard saturation function (as opposed to the generic class of nonlinearities studied in the paper of Chitour, et al.).

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BibTex Entry

@InProceedings{,: author = {Romanchuk B. G.},; title = {Notes on the Computation of the Incremental Gain of Linear Systems with Saturation. },; booktitle = {Proceedings of the 34th IEEE CDC},; year = {1995}
}



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