The input-output version of the Aizerman-Myshkis problem for retarded systems

Non-linear retarded systems are considered. Conditions for the input-output stability are derived. They are formulated in terms of the zeros of the corresponding quasi-polynomials. In addition, it is proved that retarded systems with positive impulse (Green) functions satisfy the Aizerman-Myshkis conjecture in the input-output version.