Interconnection of nonlinear causal systems

For nonlinear systems it is not a mathematically obvious fact that the simplest feedback system yields equations which are solvable, even when the gain in the loop is ⩽1. The authors treat this and more general issues. For example, it is not known (for a continuous-time system) if unity feedback for a plant C with gain <1 produces a well-posed system. It is shown that if the gain of C is <1 and C also loses sufficient efficiency at high frequency, then indeed the feedback system is well posed. The hypothesis that the gain of C is <1 can be replaced by the reasonable assumption that C saturates on large enough signals, and well posedness is still obtained. This approach also applies directly to electrical circuit connections. It is proved that rather general connections of amplifiers are well posed under the assumption that the amplifiers saturate and that they lose efficiency at high frequency