Frequency criteria for exponential stability

Abstract We discuss some frequency-domain criteria for the exponential stability of nonlinear feedback systems based on Popov’s hyperstability theorem. The main results are new bounds convergence rates perturbations damped harmonic oscillator, including Hessian-damped case, when satisfy certain sectoriality or convexity hypotheses. also include a simplified proof theorem in its general form, which has virtue that it often applies at margins other typically degenerate.