Frequency domain stability inequalities for nonlinear time delay systems

Motivated by various applications, among which one can mention the problem of PIO - P(ilot)-I(n-the-loop)-O(scillations), it is considered the problem of the absolute (global asymptotic) stability of the zero equilibrium for systems with slope restricted nonlinearities. Since the linear part incorporates also time delay, it is taken the approach of integral equations subject to the so-called IQC - Integral Quadratic Constraints. It is thus obtained an early stability inequality due to V.A. Yakubovich, but valid for time delay systems in the basic (stable) case - when the linear part is exponentially stable.