New IQC for quasi-concave nonlinearities

A new set of integral quadratic constraints (IQC) is derived For a class of rate limiters', modelled as a series connections of saturation-like memory less nonlinearities followed by integrators, The result, when used within t he standard IQC framework (in particular, with finite gain/passivity-based argiments, Lyapunov theory, structured singular values, etc.), is expected to be widely useful in nonlinear system analysis. For example, it enables ' discrimination' between 'saturation-like' and 'deadzone-like' nonlinearitie s and can be used to prove stability of systems with saturation in cases wh en replacing the saturation block by another memoryless nonlinearity with e quivalent slope restrictions makes the whole system unstable. In particular , it is shown that the L-2 gain of a unity feedback system with a rate limi ter in the forward loop cannot exceed root2. In addition, a new, more flexible version of the general IQC analysis frame work is presented, which relaxes the homotopy and boundedness conditions, a nd is more aligned with the language of the emerging IQC software. Copyrigh t (C) 2001 John Wiley & Sons, Ltd.