Delay-independent stability for interconnected nonlinear systems with finite L2 gain

In this paper delay-independent stability of a feedback interconnection of nonlinear systems with finite L₂- gain is studied. We show that the classical small-gain condition allows stability of the feedback connection independent of the constant delay. In the case of time-varying delays, a modified small-gain condition dependent on the maximum rate of change of the delay is proposed to ensure delay-independent stability. The results are immediately applicable to output-strictly passive systems. If the nonlinear systems are passive, scattering theory can be used to provide delay-independent stability when the delays are constant. To handle time-varying delays, a modified scattering transformation approach is developed to ensure delay-independent stability of the closed loop system. A numerical example is also presented to verify the efficacy of the proposed algorithms.