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

Conditions for the non-existence of the incremental `p gain of single input discrete time linear systems with saturation is presented, as well as algebraic tests for bounding the induced `2 and L2 gains. These algebraic tests are found to be the same as those which would arise if one were to conservatively use a quadratic dissipation function to bound the induced 2-norm. Keywords: nonlinear H1 control, systems with saturation, linear matrix inequalities. 1 Introduction 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; see [3],[6] for examples of such analysis. 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 a..