gain bounds for systems with sector bounded and slope‐restricted nonlinearities

This paper proposes a new method for calculating a bound on the gain of a system comprising a linear time invariant part and a static nonlinear part, which is odd, bounded, zero at zero and has a restriction on its slope. The nonlinear part is also assumed to be sector bounded, with the sector bound being (possibly) different from that implied by the slope restriction. The computation of the gain bound is found by solving a set of linear matrix inequalities, which arise from an integral quadratic constraint formulation of a multiplier problem involving both Zames‐Falb and Popov multipliers. Examples illustrate the effectiveness of the results, and comparisons are made against the state‐of‐the‐art. Copyright © 2011 John Wiley & Sons, Ltd.