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This paper proposes a method for computing finite regions of exponential stability from solutions of the absolute stability problem. A best quadratic estimate of the regions is found for a class of nonlinear characteristics which belong to a modified Lur’e sector. For a class of nonautonomous differential equations, a bound on the forcing function is found which guarantees that all the corresponding solutions remain inside the computed region.

Regions of exponential stability for the problem of Lur’e / Bereiche der exponentiellen Stabilität beim Problem von Lurje