Input-output stability of nonlinear nonautonomous systems

Stability of nonlinear nonstationary systems has been discussed by many authors. The basic method for the stability analysis is the Lyapunov functions one. By this method many strong results are obtained. But finding Lyapunov's functions for nonautonomous systems is usually a difficult task. Explicit input-output stability conditions for a class of nonlinear nonstationary systems with separated linear parts are derived. Particularly they are formulated in terms of the Hurwitzness of auxiliary matrices.