New IQC for quasi-concave nonlinearities

A set of integral quadratic constraints (IQC) is derived for a class of “rate limiters”, modelled as a series connections of saturation-like memoryless nonlinearities followed by integrators. The result, when used within the standard IQC framework, is expected to be widely useful in nonlinear system analysis. For example, it enables “discrimination” between “saturation-like” and “deadzone-like” nonlinearities and can be used to prove stability of systems with saturation in cases when replacing the saturation block by another memoryless nonlinearity with equivalent slope restrictions makes the whole system unstable. In particular, it is shown that the L₂ gain of a unity feedback system with a rate limiter in the forward loop cannot exceed √2