Absolute stability criteria with prescribed decay rate for finite-dimensional and delay systems

We provide here an extension of Popov criterion, permitting to check exponential stability with prescribed decay rate (otherwise called α-stability) of nonlinear delay systems with sector-bounded nonlinearities. As for the celebrated result, the main hypothesis is expressed under a frequency form. For the delay-free case, the latter is equivalent to a linear matrix inequality, whose solution may be found by widespread algorithms.