About stability on bounded domains of the state space

Modern aircraft control systems contain the so-called rate limiter elements which are in fact incorporating the saturation function which is a bounded nonlinearity. In certain critical cases the so-called sector rotation a standard procedure in absolute stability leads to the fact that the sector conditions are broken outside a bounded domain. In order to apply standard results of the absolute stability theory there will be combined the results of the hyperstability theory with those arising from Liapunov function theory since existence of a Liapunov function is up to now the best way to estimate stability domains. At the same time the stability conditions will be expressed in the language of some frequency domain inequality as required by the conditions of the practical problem that generated the mathematical one. AMS Classification: 93D10, 34D20, 34D23